M. Kifer and E. L. Lozinskii, "A logic for reasoning with inconsistency," Journal of Automated Reasoning 9(2), pp.179--215, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in these systems were defined in different ways. Some were based on checking which abnormal formulas (such as : are satisfied in the models of a theory (see e.g. Priest, 1991; Batens, 1998] Others were based on preferences between the truth values that are assigned to formulas (see e.g. [Kifer and Lozinskii, 1992; Arieli and Avron, 2000a] Preferential systems were also used for providing semantics for nonmonotonic consequence relations (see e.g. Shoham, 1987; Kraus et al. 1990; Makinson, 1994] It was discovered, however, that in order for them to fulfill all the desired theoretical properties that ....

.... They were also used, apparently independently at first, for constructing systems for reasoning with inconsistencies (and other abnormalities) in a way which is on the one hand non trivial and on the other hand not as weak as monotonic substructural logics (see e.g. Batens, 1986; Priest, 1991; Kifer and Lozinskii, 1992; Arieli and Avron, 1996] Interestingly, these ideas, which were developed from motivations different from stopperedness, will provide us with methods for constructing stoppered preferential systems. Following [Makinson, 1994; Lehmann, 1992] For the purpose of showing the results in ....

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M. Kifer and E. L. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 9(2):179--215, 1992.

....correct answers, and are characterized [2] as ordinary answers that can be obtained from ##### minimally repaired version of the database. In this paper we address the problem of specifying those repaired versions as the minimal models of a theory written in ######### ######### ##### [27]. It is also shown how to specify database repairs using disjunctive logic program with annotation arguments and a classical stable model semantics. Those programs are then used to compute consistent answers to general rst order queries. Both the annotated logic and the logic programming ....

....must include information about (from) the database and the information contained in the ICs. Since these two pieces of information may be mutually inconsistent, we need a logic that does not collapse in the presence of contradictions. A non classical logic, like AnnotatedPredicate Calculus (APC) [27], for which a classically inconsistent set of premises can still have a model, is a natural candidate. In [3] a new declarative semantic framework was presented for studying the problem of query answering in databases that are inconsistent with respect to universal integrity constraints. This was ....

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Kifer, M. and Lozinskii, E.L. A Logic for Reasoning with Inconsistency. ####### ## ##################, 1992, 9(2):179-215.

....is often too weak. In fact, since Belnap s logic is weaker than classical logic w.r.t. consistent theories , we are even in a worse situation than in classical logic A (partial) solution to this problem is by using preferential reasoning in the context of multiplevalued logic (see, e.g. [1, 2, 3, 4, 16, 17, 25, 26]) At the computational level, implementing paraconsistent reasoning based on four valued semantics poses important challenges. An e ective implementation of theorem provers for one of the existing proof systems for Belnap s logic requires a major e ort. The problem is even worse in the context ....

.... be traced back to [22] Furthermore, this approach is the semantical basis of some wellknown general patterns for non monotonic reasoning, introduced in [18, 19, 20, 21] and it is a key concept behind many formalisms for nonmonotonic and paraconsistent reasoning, such as Kifer and Lozinskii s RI [16, 17], Arieli and Avron s bilattice based logics [1, 4] and Priest s LPm [25, 26] Our purpose in this paper is to propose techniques of expressing some of the preferential relations used in these formalisms by formulae in the underlying language. Next we de ne the framework for doing so. 2.2 The ....

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M.Kifer, E.L.Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning 9(2), pp. 179-215, 1992.

....= kafka as a consistent answer. Notice that repairs are obtained by insertion deletion of whole relational tuples, and we do not specify a preference for any particular kind of repairs. Repairs are just used to characterize the consistent answers. Annotated Predicate Calculus was introduced in [24]. It constitutes a non classical logic where classical inconsistencies may be accommodated without trivializing reasoning. Its syntax is similar to that of classical logic, except for the fact that atoms are annotated with values drawn from a truth values lattice. In [3] in order to embed the ....

Kifer, M. and Lozinskii, E.L. \A Logic for Reasoning with Inconsistency". Journal of Automated reasoning, 1992, 9(2):179-215.

....is often too weak. In fact, since Belnap s logic is weaker than classical logic w.r.t. consistent theories, we are even in a worse situation than in classical logic A (partial) solution to this problem is by using preferential reasoning in the context of multiple valued logic (see, e.g. [1 3, 11, 12, 20, 21]) At the computational level, implementing paraconsistent reasoning based on four valued semantics poses important challenges. An e ective implementation of theorem provers for one of the existing proof systems for Belnap s logic requires a major e ort. The problem is even worse in the context ....

.... is a very natural one, and may be traced back to [17] Furthermore, this approach is the semantical basis of some well known general patterns for non monotonic reasoning, introduced in [13 16] and it is a key concept behind many formalisms for nonmonotonic and paraconsistent reasoning (see, e.g. [1 3, 11, 12, 20, 21]) Our purpose in this paper is to propose techniques of expressing preferential reasoning by formulae in the underlying language. Next we de ne the framework for doing so. For a longer version of this paper see [4] O.Arieli and M.Denecker 2.2 The underlying semantical structure The ....

M.Kifer, E.L.Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning 9(2), pp.179-215, 1992.

....may remain inconsistent, but the set of conclusions implied by it is not explosive, i.e. not every fact follows from an inconsistent database. Paraconsistent procedures for integrating data (e.g. 14, 41] are often based on a paraconsistent reasoning process, such as LFI [13] annotated logics [30, 40], or other non classical proof systems [5, 37] Coherent (consistency base) methods, in which the amalgamated data is revised in order to restore consistency (see, e.g. 6, 8, 11, 25, 31] In many cases the underlying formalism of these approaches are closely related to the theory of belief ....

.... such as con dence factors, amount of belief for or against a speci c assertion, etc. These approaches combine corresponding formalisms of knowledge representation (such as annotated logic programs [40, 41] or bilattice based logics [5, 21, 33] together with non classical refutation procedures [20, 30, 40] that allow to detect inconsistent parts of a database and maintain them. A closely related topic is the problem of giving consistent query answers in inconsistent database [3, 10, 25] The idea is to answer database queries in a consistent way without computing the repairs of the database. There ....

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M.Kifer, E.L.Lozinskii. A logic for reasoning with inconsistency. J. Automated Reasoning 9(2), pp.179-215, 1992.

....correct answers, and are characterized [2] as ordinary answers that can be obtained from every minimally repaired version of the database. In this paper we address the problem of specifying those repaired versions as the minimal models of a theory written in Annotated Predicate Logic [27]. It is also shown how to specify database repairs using disjunctive logic program with annotation arguments and a classical stable model semantics. Those programs are then used to compute consistent answers to general rst order queries. Both the annotated logic and the logic programming ....

....must include information about (from) the database and the information contained in the ICs. Since these two pieces of information may be mutually inconsistent, we need a logic that does not collapse in the presence of contradictions. A non classical logic, like Annotated Predicate Calculus (APC) [27], for which a classically inconsistent set of premises can still have a model, is a natural candidate. In [3] a new declarative semantic framework was presented for studying the problem of query answering in databases that are inconsistent with respect to universal integrity constraints. This was ....

[Article contains additional citation context not shown here]

Kifer, M. and Lozinskii, E.L. A Logic for Reasoning with Inconsistency. Journal of Automated reasoning, 1992, 9(2):179-215.

....from classical logic, moving to non classical logic, where reasoning in the presence of classical inconsistencies does not necessarily collapse. Following [8] we show here how to generate a consistent first order theory with a non classical semantics. We use Annotated Predicate Calculus (APC) [67]. In APC, database atoms are annotated with truth values taken from a truth value lattice. The most common annotations are: true (t) false (f ) contradictory (#) and unknown (#) In [8] a lattice was used to capture the preference for integrity constraints when they conflict with the data: the ....

....is (p and the database contains the facts p and q. In the approach of Lin [78] p q can be inferred (minimal change is captured correctly) but p, q and (p can no longer be inferred (they are all involved in an inconsistency) # Several papers by Lozinskii, Kifer, Arieli and Avron [9,67,81] studied the problem of making inferences from a possibly inconsistent, propositional or first order, knowledge base. The basic idea is to infer the classical consequences of all maximal consistent subsets of the knowledge base [81] or all most consistent models of the knowledge base [9,67] where ....

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M. Kifer and E. L. Lozinskii. A Logic for Reasoning with Inconsistency. Journal of Automated Reasoning, 9(2):179--215, 1992.

....from CNPq (Brazil) Author (3) was supported by the Research Fund of Ghent University, project BOF2001 GOA 008. and inconsistency management has been done during the last decade. Two basic approaches have been followed in solving the inconsistency problem in knowledge bases : belief revision ([21, 22]) and paraconsistent logic ( 10, 12, 6] The goal of the first approach is to make an inconsistent theory consistent, either by revising it or by representing it by a consistent semantics. So, the main concern there is to avoid contradictions. On the other hand, the paraconsistent approach allows ....

Kifer, M., Lozinskii, E.L : A Logic for Reasoning with Inconsistency. Journal of Automated Reasoning 9 : 179-215, 1992.

....the consistent answers. The only commitment at this point is that repairs are obtained by insertion deletion of whole relational tuples. Later on we make some considerations on the possibility of having more flexible repairs (see also [4, 11] Annotated Predicate Calculus was introduced in [25]. It constitutes a non classical logic where classical inconsistencies may be accommodated without trivializing reasoning. Its syntax is similar to that of classical logic, except for the fact that atoms are annotated with values drawn from a truth values lattice. In [3] in order to embed the ....

Kifer, M. and Lozinskii, E.L. "A Logic for Reasoning with Inconsistency". Journal of Automated reasoning, 1992, 9(2):179-215.

....a given set of integrity constraints are characterized [2] as ordinary answers that can be obtained from every repaired version of the database. In this paper we address the problem of specifying the repairs of a database as the minimal models of a theory written in Annotated Predicate Logic [10]. The speci cation is rst transformed into a disjunctive logic program with annotation arguments and then, from the program, consistent answers to rst order queries are obtained. 1 Introduction Integrity constraints (ICs) are important in the design and use of a relational database. They ....

....semantic framework was presented for studying the problem of query answering in databases that are inconsistent with integrity constraints. This was done by embedding both the database instance and the integrity constraints into a single theory written in Annotated Predicate Calculus (APC ) [10] with an appropriate non classical truth values lattice Latt . In [3] it was shown that there is a one to one correspondence between some minimal models of the annotated theory and the repairs of the inconsistent database for universal ICs. In this way, a logical speci cation of the database ....

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Kifer, M. and Lozinskii, E.L. \A Logic for Reasoning with Inconsistency". Journal of Automated reasoning, 9(2):179-215, November 1992.

....constraints are characterized [Arenas et al. 1999] as ordinary answers that can be obtained from every repaired version of the database. In this paper we address the problem of specifying the repairs of a database as the minimal models of a theory written in Annotated Predicate Logic [Kifer et al. 1992a] The speci cation is then transformed into a disjunctive logic program with annotation arguments and a stable model semantics. From the program, consistent answers to rst order queries are obtained. 1 Introduction Integrity constraints (ICs) are important in the design and use of a ....

....The speci cation must include information about (from) the database and the information contained in the ICs. Since these two pieces of information are mutually inconsistent, we need a logic that does not collapse in the presence of contradictions. A logic like Annotated Predicate Logic (APC) [Kifer et al. 1992a] for which a classically inconsistent set of premises can still have a model, is a natural candidate. In [Arenas et al. 2000a] a new declarative semantic framework was introduced for studying the problem of query answering in databases that are inconsistent with integrity constraints. This ....

[Article contains additional citation context not shown here]

Kifer, M. and Lozinskii, E.L. \A Logic for Reasoning with Inconsistency". Journal of Automated reasoning, 9(2):179-215, November 1992.

....; 1915 ) does not have true as a consistent answer, because it is not true in every repair. Query Q 2 (y) 9x9zBook(x ; y ; z ) has y = metamorph as a consistent answer. Query Q 3 (x) 9zBook(x; metamorph ; z) has x = kafka as a consistent answer. 2 Annotated Predicate Calculus was introduced in [18]. It constitutes a non classical logic where classical inconsistencies may be accommodated without trivializing reasoning. Its syntax is similar to that of classical logic, except for the fact that atoms are annotated with values drawn from a truth values lattice. In [3] in order to embed the ....

Kifer, M. and Lozinskii, E.L. \A Logic for Reasoning with Inconsistency". Journal of Automated reasoning, 1992, 9(2):179-215.

.... data over another [2, 4, 5] Other approaches are based on rewriting rules for representing the information in a speci c form [14] or use multiple valued semantics (e.g. annotated logic programs [28, 29] and bilattice based formalisms [12, 22] together with non classical refutation procedures [11, 19, 28] that allow to decode within the language itself some meta information such as con dence factors, amount of belief for against a speci c assertion, etc. Each one of the techniques mentioned above has its own limitations and or drawbacks. For instance, in order to properly translate the ....

M.Kifer, E.L.Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning 9(2), 179-215, 1992.

....from classical logic, moving to non classical logic, where reasoning in the presence of classical inconsistencies does not necessarily collapse. Following [8] we show here how to generate a consistent first order theory with a non classical semantics. We use Annotated Predicate Calculus (APC) [50]. In APC, database atoms are annotated with truth values taken from a truthvalue lattice. The most common annotations are: true (t) false (f ) contradictory (#) unknown (#) In [8] an extended lattice was used to capture the preference for ICs when they conflict with the data: ICs cannot be ....

....is q) and the database contains the facts p and q. In the approach of Lin [60] p q can be inferred (minimal change is captured correctly) but p, q and q) can no longer be inferred (they are all involved in an inconsistency) # Several papers by Lozinski, Kifer, Arieli and Avron [63, 50, 9] studied the problem of making inferences from a possibly inconsistent, propositional or firstorder, knowledge base. The basic idea is to infer the classical consequences of all maximal consistent subsets of the knowledge base [63] or all most consistent models of the knowledge base [50, 9] where ....

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Kifer, M. and Lozinskii, E.L. A Logic for Reasoning with Inconsistency. Journal of Automated Reasoning, 1992, 9(2):179--215.

....1. introduce additional truth values to alter the semantics [2, 4, 8, 16] 2. introduce additional semantic parameters such as nonstandard possible worlds, setups or situations to evaluate formulae [10, 17, 19] 3. introduce labels or annotations into formulae to represent inconsistencies [9, 13, 15] Undoubtedly, many semantic and syntactic innovations are involved in these approaches; nonetheless, they are in agreement with the standard account of reasoning in terms of truth preservation. In contrast, Jennings et al. [12] have proposed a more general and pragmatic account of reasoning ....

M. Kifer and E. L. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 9:179--215, 1992.

....of first order formulae by simply restricting them to clausal form. This is particularly interesting in light of recent developments in non Horn clause logic programming and deductive databases where boolean negation is permitted to appear in the head and the body of a clause ( 3] 6] 7] 9] [10], 17] It is thus possible for a logic program or a database to be inconsistent, and if a classical deductive procedure is adopted, any conclusion can be deduced (since A; A B is a valid inference in classical logics) One very natural strategy to prevent inferential explosion is to view an ....

M. Kifer and E. L. Lozinskii. A logic for reasoning with inconsistency. Journal Of Automated Reasoning, 9:179--215, 1992.

....Abe [1] and da Costa, Subrahmanian and Vago [5] They show that almost all the basic results of classical model theory can be adapted to these systems. In this paper we follow the axiomatization of PL given in [5] and refer to this paper for the properties of PL that we use. Kifer and Lozinkii in [9] introduce a rst order annotated logic (APC) with a sound and complete proof procedure, and apply it to several non monotonic reasoning arguments. Like most, but not all, paraconsistent logics PL fails to be structural. The source of this diculty is the dichotomy between the formulas for which ....

Kifer, M. and Lozinskii, E. L., A Logic for Reasoning with Inconsistency, Journal of Automated Reasoning 9 (1992), 179-215.

....programs using Belnap s four valued logic [4] The result was generalized by Subrahmanian [32] to programs possibly containing disjunctive information. Recently, the paraconsistent logic programming framework is further extended to treat default negation along with explicit negation in a program [28, 35, 21, 17]. However, in the context of extended disjunctive programs, a suitable paraconsistent extension of the answer set semantics has not been studied in the literature. In this paper, we present declarative semantics of possibly inconsistent ex2 tended disjunctive programs. We introduce the ....

....employ Belnap s four valued logic as a theoretical basis, but their framework does not treat default negation in a program. Fitting [12] provides a general framework for logic programming in terms of bilattices, but he does not discuss programs containing two kinds of negation. Kifer and Lozinskii [21] extend Blair and Subrahmanian s annotated logic programming framework to 23 a theory possibly containing default negation, and Wagner [35] also develops a theory of inconsistent logic programs with two kinds of negation. Compared with our approach, they do not treat disjunctions in a program and ....

M. Kifer and E. L. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 9, 179-215, 1992.

.... order for j= 4 I1 obtains by taking as the only maximal element (and all the other truth values are incomparable) The preferential order for j= 4 I2 obtains by taking and as greater than t and f (see [2] for a justification of these choices) ffl The logic RI of Kifer and Lozinskii [9]: This is an annotated logic [22] The preferred models of RI minimize the assignments w.r.t. a certain set Delta aeL. Thus, the preferential order in this case obtains by considering every element in Delta as strictly greater than every element in Ln Delta. 4 Useful properties of j= L;D ....

....for commonsense reasoning. It is shown that the consequence relations that are obtained in this way have several useful properties that are important for applications of logic in AI, where uncertainty, inconsistency, and nonmonotonicity have a central role. Such cases are considered, e.g. in [2, 9, 13, 19]. Further applications will be considered in a future work. Acknowledgement This work is supported by the visiting postdoctoral fellowship FWO Flanders. ....

M.Kifer, E.L.Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning 9(2), pages 179--215, 1992.

....Annotated logic Programming (GAP) discussed next, Kifer and Subrahmanian [15] solved several of these problems. Kifer and Subrahmanian [15] proposed the GAP framework as a unifying framework which generalizes various results and treatments of temporal and multi valued logic programming, e.g. [2, 10, 14, 26, 30]. A main di erence between GAP and any IB framework, including ours, is clearly in the approach. The two approaches have their own advantages and disadvantages, as discussed in Section 1. In terms of expressive power, GAP can simulate the computation of some IB frameworks. 3 As the semantics ....

Kifer M. and Lozinskii E.L. A logic for reasoning with inconsistency. In Proc. 4th IEEE Symp. on Logic in Computer Science (LICS), pages 253-262, Asilomar, CA, 1989. IEEE Computer Press.

....in these systems were defined in different ways. Some were based on checking which abnormal formulas (such as : are satisfied in the models of a theory (see e.g. Priest, 1991; Batens, 1998] Others were based on preferences between the truth values that are assigned to formulas (see e.g. [Kifer and Lozinskii, 1992; Arieli and Avron, 2000a] Preferential systems were also used for providing semantics for nonmonotonic consequence relations (see e.g. Shoham, 1987; Kraus et al. 1990; Makinson, 1994] It was discovered, however, that in order for them to satisfy all the desired theoretical properties that ....

....relations. They were also used, apparently independently at first, for constructing systems for reasoning with inconsistencies (and other abnormalities) in a way which is on the one hand non trivial and on the other hand not as weak as monotonic substructural logics (see e.g. Priest, 1991; Kifer and Lozinskii, 1992; Batens, 1998] Interestingly, these ideas, which were developed from motivations different from stopperedness will provide us with methods for constructing stoppered preferential systems. 4 Formula Preferential Systems Formula preferential systems are a generalization of the ....

M. Kifer and E. L. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 9(2):179--215, 1992.

....that some well known plausible nonmonotonic logics can be constructed using this method. Most of these logics are paraconsistent as well (these include some logics that we have considered in previous works [2, 3, 5] 2 This is a common method for dealing with inconsistent theories see, e.g. [13, 14, 15, 20, 21, 23, 34, 35, 39, 42, 43]. General Patterns for Nonmonotonic Reasoning 121 2 Preferential systems from an abstract point of view In this section we investigate preferential reasoning from an abstract point of view. First we briefly review the original treatments of Makinson [28] and Kraus, Lehmann, and Magidor [24] ....

....on the left. A discussion and some justification appears in [24, 27] 4 A stronger intuitive justification will be given below, using more general frameworks. 2.2 Generalizations In the sequel we will consider several generalizations of the basic theory presented above: 1. In their formulation, [23, 24, 28, 29] consider the classical setting, i.e. the basic language is that of the classical propositional calculus (# cl ) and the basic entailment relation is the 3 A conditional assertion in terms of [24] 4 Systems that satisfy the conditions of Definitions 2.1, 2.2, as well as other related ....

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M.Kifer, E.L.Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning. Vol.9, No.2, pages 179--215, 1992.

....I 0 : assume declare p(2) for p. Then I(p) is functional i not both I j= p(fig) and I j= p(fjg) for i 6= j i p(fig) p(fjg) 6= p( i I 0 (p) 6= h;i. Consider the IV MGTP program P = f p(f1g) p(f2g)g. It is neither satis able nor e satis able. In paraconsistent reasoning [14], however, one infers from it the atom p( indicating that inconsistent information is entailed about p. Lifting the non emptiness restriction on e interpretations still gives a well de ned, non trivial semantics and captures paraconsistent reasoning [17] What must be changed in the IV MGTP ....

M. Kifer and E. L. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 9(2):179-215, Oct. 1992.

....on logic programming which follow, or enable, the potential contradictions view. Unfortunately we cannot consider in this survey, with the same detail, all extant semantics for paraconsistent logic programs (extended or otherwise) Notable cases are the annotated logic programs extensions in [26, 27], with the exception of [8] Fitting s semantics [16, 17] also will not be addresed in great detail. Still, in Section 8, we briefly describe the most important features of these and other related works. Finally, we collect, in the last section, the main conclusions of our comparative study. For ....

....not :a respectively entail B:a and Ba, i.e. in truthvale IV one simultaneously believes in the falsity of :a and in the truth of a. This form of inconsistency is known in the paraconsistency literature as epistemic contradiction, which does not raise any problem from a conceptual point of view [49, 44, 26]. In other works [ the reading of the default negation operator is :B and therefore the simultaneous truth of not a and not :a is understood as :Ba and :B:a, i.e. in truth value IV one does not believe in neither the truth of a nor the falsity of a, which is not inconsistent unless one ....

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M. Kifer and E. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 8:179--215, 1992.

....such as satis ability and consistency, require minor adjustments) Having is convenient because it provides a degree of tolerance to inconsistency that may exist between database states and views over them. 12 It is also a simple adaptation of techniques used in paraconsistent logics (e:g: KL92] which analyze the knowledge contained in inconsistent states. The reader is referred to [BK95; BK94] for further discussion. LOGIC FOR TRANSACTIONS 23 As described in Section 1.3, T R comes with a language, L (which determines the syntax of formulas) and with a pair of oracles, O d and O ....

M. Kifer and E.L. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 9(2):179-215, November 1992.

....have been implemented in the language C for experimentation[30] One is based on signed resolution, and the other is based on CLP. We are especially interested in comparing the structure of the search space induced by each of the query processing methods. Annotated logic, as studied in [4] 17] [18], 19] has been shown to relate to signed formulas [23] In [20] a query processing procedure for annotated logic programming was introduced that shares certain characteristics with the signed resolution procedure developed in this paper. In particular, since the signed atom resolved upon in ....

M. Kifer and E. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 9:179--215, 1992.

....neither variant nor term subsumption operations. This requirement may occur not only with delay lists for X clauses where clause subsumption [10] appears to be needed, but also if constraints of CLP(X) style [35] are tabled or if generalized resolution methods such as Annotated Predicate Calculus [39, 38] are implemented. Incorporating these paradigms with SLG forms a task for which the semantic underpinnings as yet are incomplete. 29] discussed the incorporation of constraints and OLDT under a resolution method called OLDTC, but these results have not been extended to full SLG. On an ....

M. Kifer and E.L. Lozinskii. A logic for reasoning with inconsistency. J. Automated Reasoning, 9(2):179--215, 1992.

....in finitely valued logics based on semi lattices, and Hahnle [9] who derived tableau style axiomatizations of distribution quantifiers by using Birkhoff s representation theorem for finite distributive lattices. Methods for automated proving in paraconsistent or annotated logics (cf. e.g. [11]) also have similarities with our approach in the case of finitely valued logics. Known methods from modal logic seem to occur as particular cases of general concepts such as those considered here (see also [5] 14] 7 Conclusions In this paper we showed that the Priestley duality for ....

M. Kifer and M. Lozinskii. A logic for reasoning with inconsistency. J. Automated Reasoning, 9:179--215, 1992.

....in the work of H ahnle [H ah93, H ah94, H ah96b] who, instead of single truth values, uses sets of truth values as signs for the literals, and de nes various versions of signed resolution. For more details on signed resolution we refer to [BFS99] We also refer to the work of Kifer and Lozinskii [KL92] and Lu, Murray and Rosenthal [LMR93, LMR98] where signed resolution is discussed, also in the context of annotated logic. Concerning non clausal methods in many valued logics, here we only mention tableaux methods such as the method of Surma [Sur84] further developed by Carnielli [Car87] see ....

....and i = fj 2 A j j ig. Second, the fact that the signs of the clauses all have the special form mentioned above, allows a reduction of the number of clauses that may be generated in the resolution process compared to other approaches that use sets as signs, and even with approaches such as [KL92] where the signs are i or complements thereof, where i is an arbitrary element of the lattice of truth values. Moreover, we show that certain re nements of classical 2 resolution such as hyperresolution (which have been extended to regular logics in [H ah94, H ah96b] can be extended to sets of ....

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M. Kifer and M. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 9:179-215, 1992.

....in finitely valued logics is the many valued resolution method by Baaz and Fermuller [1] Their results have been extended in [7, 8] 10] and [2] where various versions of signed resolution are defined. Signed resolution rules have also been proposed for annotated logics by Kifer and Lozinskii [9] and Lu, Murray and Rosenthal [10] Hahnle [8] has developed a hyper resolution method for the so called regular logics which is directly modeled after classical hyperresolution. The completeness proofs are more or less directly derived from those for classical logic. The calculi in [10] are ....

....logics. With this method the previous results on automated theorem proving for many valued logics can be greatly improved. i) Apart from reconstructing known completeness results for existing methods, including many valued resolution [1] regular hyper resolution [8] and annotated resolution [9, 10], the inference systems which we obtain are much more restricted, in particular by ordering constraints and selection functions. ii) The specialization of the general chaining inference systems is very direct and does not involve any sophisticated encodings. iii) The general concept of ....

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M. Kifer and M. Lozinskii. A logic for reasoning with inconsistency. J. of Automated Reasoning, 9:179--215, 1992.

....[3, 5] or Disjunctive Logic Programs under various semantics. ffl Tabling can be used as a preprocessor for stable models and extensions [56, 57] or can compute these models directly by means of abduction [34, 6] ffl Tabling can be used as a means to aggregate solutions for annotation logics [74], 75] 89] 115] 41] 35] or preference logics [58] 29] 4 Overview ffl A (very partial ) bibliography Formulations of Tabling: 48] 19] 122] 46] 71] 112] 128] 132] 23] 40] 81] 123] 24] 21] 32] 82] 53] 64] 134] 16] 13] 17] 18] 119] 110] ....

M. Kifer and E.L. Lozinskii. A logic for reasoning with inconsistency. J. Automated Reasoning, 9(2):179--215, 1992.

....Abe [1] and da Costa, Subrahmanian and Vago [5] They show that almost all the basic results of classical model theory can be adapted to these systems. In this paper we follow the axiomatization of PL given in [5] and refer to this paper for the properties of PL that we use. Kifer and Lozinkii in [9] introduce a first order annotated logic (APC) with a sound and complete proof procedure, and apply it to several non monotonic reasoning arguments. Like most, but not all, paraconsistent logics PL fails to be structural. The source of this difficulty is the dichotomy between the formulas for ....

Kifer, M. and Lozinskii, E. L., A Logic for Reasoning with Inconsistency, Journal of Automated Reasoning 9 (1992), 179--215.

....first order logic provides an appropriate formal tool for modeling them. Other semantic inferences, such as Birds typically fly and Politicians are liars, are defeasible. Many different approaches have been designed to deal with this type of reasoning: those of Reiter (1980) Ginsberg (1988) and Kifer and Lozinskii (1992) are only a few. In contrast with semantic inferences, which are triggered by commonsense knowledge, pragmatic inferences are derived from general rules that govern the use of language. They can be lexical in nature, as in the case of a factive (Kiparsky Kiparsky 1971) syntactic, as in the ....

....(examples (1) 4) We believe that most formalisms that have been proposed in the knowledge representation literature have been designed to address only the first of these requirements. Both justification based (Reiter 1980; Brewka 1994; Delgrande 1994) and multivalued based (Ginsberg 1988; Kifer Lozinskii 1992) theories define satisfaction so that defeasible information is always cancelled by entailments or so that weaker defeasible information is always cancelled by stronger defeasible information. Although such a definition could account for the inferences that are most likely to be drawn from ....

Kifer, M., and Lozinskii, E. 1992. A logic for reasoning with inconsistency. Journal of Automated Reasoning 9(2):179--215.

....then OE j 0 . cautious cut: if j 0 OE and OE j 0 , then j 0 . left logical equivalence: if cl OE and j 0 , then OE j 0 . right weakening: if cl , OE and j 0 , then j 0 OE. 2 This is a common method for dealing with inconsistent theories see, e.g. [13, 14, 15, 20, 21, 23, 34, 35, 39, 42, 43]. 3 A conditional assertion in terms of [24] 3 Definition 2 [24] A cumulative relation j 0 is called preferential if it is closed under the following rule: introduction (Or) if j 0 and OE j 0 , then OE j 0 . Note In order to distinguish between the rules of Definitions 1, ....

....the left. A discussion and some justification appears in [24, 27] 4 A stronger intuitive justification will be given below, using more general frameworks. 2.2 Generalizations In the sequel we will consider several generalizations of the basic theory presented above: 1. In their formulation, [23, 24, 28, 29] consider the classical setting, i.e. the basic language is that of the classical propositional calculus ( Sigma cl ) and the basic entailment relation is the classical one ( cl ) Our first generalization concerns with an abstraction of the syntactic components and the entailment relations ....

[Article contains additional citation context not shown here]

M.Kifer, E.L.Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning. Vol.9, No.2, pages 179--215, 1992. 32

....Kifer and coworkers. Besides the capability of providing an efficient approach to paraconsistent reasoning, this logic allows to formalize and to implement a flexible inference machine incorporating temporal and uncertain reasoning methods. For a comprehensive description the reader may refer to [12, 11]. Annotated clause: p : l p 1 : l 1 : p k : l k not(B k 1 : l k 1 ) not(B k n : l k 1 ) The literals p; p i are from a function symbol free language L. The l i s are called annotations and are constants or variables from a complete lattice T 1 of truth values. Semantics: ....

....examples of how GAP can be used in the context of distributed knowledge bases: Paraconsistent reasoning. Definite Horn clauses used in ordinary logic programming languages lack the capability to express logical inconsistencies, inherent to collaborative environment. Using bilattices like FOUR [11] we are able to explicitly represent clauses which state how to deal with conflicting knowledge, e.g. buy stock(IBM) f] buy stock opinions(IBM) if there is any inconsistency concerning the idea of buying stocks from IBM then we should better not buy it. Majority decision making. For ....

M. Kifer and E. L. Lozinskii. A Logic for Reasoning with Inconsistency. Journal of Automated Reasoning, Vol. 9, 1992, pp. 179-215

....classical member=2 predicate, written as a GAP over L 2 is: member(X; X j ] member(X; jY ] member(X;Y ) In general, we obtain an equivalence between GAPs over L 2 and definite logic programs by adding the annotation : to every predicate symbol of the latter. Example 2. [10] Consider Belnap s logic FOUR = f ; f ; t; g, f OE f ; OE t; f OE ; t OE g) The tweety example can be encoded as: f lies(X) t bird(X) t: penguin(fred) t: f lies(X) f penguin(X) t: bird(tweety) t: bird(X) t penguin(X) t: In this example we conclude that f ....

.... 0 ; Source) P rob nomenclature(Part; 0 STRUT 0 ; Source) 100; 100] The definition of the negation operator is : Low; High] 1 Gamma High; 1 Gamma Low] As originally presented [11] the GAP framework lacks a form of (nonmonotonic) default negation (called ontological negation in [10]) i.e. a nonmonotonic closed world assumption. This has been remedied in the more recent work [13] where a well founded like [8] and answer sets like semantics [9] have extended GAPs with a default negation operator. However the semantics of [13] ignores a fundamental relationship that default ....

M. Kifer and E. Lozinskii. A logic for reasoning with inconsistency. J. of Automated Reasoning, 8:179--215, 1992.

....provides an appropriate formal tool for modeling them. Other semantic inferences, such as Birds typically fly and Politicians are liars, are defeasible. Many different approaches have been designed to deal with this type of reasoning: those of Reiter [17] Ginsberg [5] and Kifer and Lozinskii [10] are only a few. In contrast with semantic inferences, which are triggered by commonsense knowledge, pragmatic inferences are derived from general rules that govern the use of language. They can be lexical in nature, as in the case of a factive [11] syntactic, as in the case of a cleft sentence ....

....when certain pragmatic inferences are cancelled (examples (1) 4) We believe that most formalisms that have been proposed in the knowledge representation literature have been designed to address only the first of these requirements. Both justification based [17, 2, 3] and multivalued based [5, 10] theories define satisfaction so that defeasible information is always cancelled by entailments or so that weaker defeasible information is always cancelled by stronger defeasible information. Although such a definition could account for the inferences that are most likely to be drawn from ....

M. Kifer and E.L. Lozinskii, `A logic for reasoning with inconsistency ', Journal of Automated Reasoning, 9 (2), 179--215, (November 1992).

....Work: Recent developments in DDBs (and logics in general) have led to frameworks capable of handling various forms of imperfection in knowledge. Abiteboul, et al. 1] Liu [16] and Dong and Lakshmanan [5] dealt with DDBs with incomplete information in the form of null values. Kifer and Lozinskii [13] have developed a logic for reasoning with inconsistency. Most of the works dealing with uncertainty in knowledge bases employ one of the following formalisms: 1) a form of fuzzy logic (programming) e.g. van Emden [20] Steger et al. 19] and Fitting [8] 2) annotated logic programming (e.g. ....

M. Kifer and E.L. Lozinskii. A logic for reasoning with inconsistency. In Proc. 4th IEEE Symp. on Logic in Computer Science, pages 253--262, Asilomar, CA, 1989.

....is ad hoc and depends on the intuition and experience of experts in a particular application context. N can be finite or countably uncountably infinite (see Section 2) 3. In case N is a partially ordered set (for example, a lattice) one may proceed similarly as in signed logic: for example, in [75, 88, 95] a literal is of the form p (or similar) where is an element of a partially ordered set P . An interpretation I satisfies (does not satisfy) p iff I(p) P (I(p) 6 P ) But in partial orders (and in lattices in particular) one has generally not P = fi j i P jg [ fi j i P jg. This fact is ....

....P . An interpretation I satisfies (does not satisfy) p iff I(p) P (I(p) 6 P ) But in partial orders (and in lattices in particular) one has generally not P = fi j i P jg [ fi j i P jg. This fact is exploited to handle inconsistency with the partial order determined by a lattice structure [75] as well as to accomodate partial knowledge [97] and some uncertainty paradigms [81] Based on the principles described above, other deduction problems have been tackled. We give examples of deduction problems which have been studied but for which neither experimental nor complexity results were ....

M. Kifer and E. L. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 9(2):179--215, Oct. 1992.

....classical member=2 predicate, written as a GAP over L 2 is: member(X; X j ] member(X; jY ] member(X;Y ) In general, we obtain an equivalence between GAPs over L 2 and definite logic programs by adding the annotation : to every predicate symbol of the latter. Example 2 [10] Consider Belnap s logic FOUR = f ; f ; t; g, f OE f ; OE t; f OE ; t OE g) The tweety example can be encoded as: f lies(X) t bird(X) t: penguin(fred) t: f lies(X) f penguin(X) t: bird(tweety) t: bird(X) t penguin(X) t: In this example we conclude that f ....

.... 0 ; Source) P rob; nomenclature(Part; 0 STRUT 0 ; Source) 100; 100] The definition of the negation operator is : Low; High] 1 Gamma High; 1 Gamma Low] As originally presented [11] the GAP framework lacks a form of (nonmonotonic) default negation (called ontological negation in [10]) i.e. a nonmonotonic closed world assumption. This has been remedied in the more recent work [13] where a well founded like [8] and answer sets like semantics [9] have extended GAPs with a default negation operator. However the semantics of [13] ignores a fundamental relationship that default ....

M. Kifer and E. Lozinskii. A logic for reasoning with inconsistency. J. of Automated Reasoning, 8:179--215, 1992.

No context found.

M. Kifer and E.L. Lozinskii. A Logic for Reasoning with Inconsistency. Journal of Automated Reasoning, 9(2):179-215, November 1992.

....known (e.g. 1] and we are not going to propose J. Lloyd et al. Eds. CL 2000, LNAI 1861, pp. 926 941, 2000. Springer Verlag Berlin Heidelberg 2000 yet another definition for consistent query answers. Instead, we introduce a new semantic framework, based on Annotated Predicate Calculus [9], that leads to a di#erent computational solution and provides a basis for a systematic study of the problem. Ultimately, our framework leads to the query semantics proposed in [1] According to [1] a tuple t is an answer to the query Q(x) in a possibly inconsistent database instance r,ifQ( t) ....

....paper, we take a more direct approach. First, since the database is inconsistent with the constraints, it seems natural to embed it into a logic that is better suited for dealing with inconsistency than classical logic. In this paper we use Annotated Predicate Calculus (abbr. APC) introduced in [9]. APC is a form of paraconsistent logic, i.e. logic where inconsistent information does not unravel logical inference and where causes of inconsistency can be reasoned about. APC generalizes a number of earlier proposals [12,11,3] and its various partial generalizations have also been studied ....

[Article contains additional citation context not shown here]

M. Kifer and E.L. Lozinskii. A Logic for Reasoning with Inconsistency. Journal of Automated Reasoning, 9(2):179--215, November 1992.

....in this case. Several proposals to address these problems both semantically and computationally are known (e.g. 1] and we are not going to propose yet another definition for consistent query answers. Instead, we introduce a new semantic framework, based on Annotated Predicate Calculus [9], that leads to a different computational solution and provides a basis for a systematic study of the problem. Ultimately, our framework leads to the query semantics proposed in [1] According to [1] a tuple t is an answer to the query Q(x) in a possibly inconsistent database instance r, if Q( ....

....paper, we take a more direct approach. First, since the database is inconsistent with the constraints, it seems natural to embed it into a logic that is better suited for dealing with inconsistency than classical logic. In this paper we use Annotated Predicate Calculus (abbr. APC) introduced in [9]. APC is a form of paraconsistent logic, i.e. logic where inconsistent information does not unravel logical inference and where causes of inconsistency can be reasoned about. APC generalizes a number of earlier proposals [12, 11, 3] and its various partial generalizations have also been studied ....

[Article contains additional citation context not shown here]

M. Kifer and E.L. Lozinskii. A Logic for Reasoning with Inconsistency. Journal of Automated Reasoning, 9(2):179--215, November 1992.

....in this case. Several proposals to address these problems both semantically and computationally are known (e.g. 1] and we are not going to propose yet another de nition for consistent query answers. Instead, we introduce a new semantic framework, based on Annotated Predicate Calculus [9], that leads to a di erent computational solution and provides a basis for a systematic study of the problem. Ultimately, our framework leads to the query semantics proposed in [1] According to [1] a tuple t is an answer to the query Q( x) in a possibly inconsistent database instance r, if Q( ....

....paper, we take a more direct approach. First, since the database is inconsistent with the constraints, it seems natural to embed it into a logic that is better suited for dealing with inconsistency than classical logic. In this paper we use Annotated Predicate Calculus (abbr. APC) introduced in [9]. APC is a form of paraconsistent logic, i.e. logic where inconsistent information does not unravel logical inference and where causes of inconsistency can be reasoned about. APC generalizes a number of earlier proposals [12, 11, 3] and its various partial generalizations have also been studied ....

[Article contains additional citation context not shown here]

M. Kifer and E.L. Lozinskii. A Logic for Reasoning with Inconsistency. Journal of Automated Reasoning, 9(2):179-215, November 1992.

....An important aspect of F logic is its extensibility it can be combined with a broad range of other specialized logics. In Section 17, we outline two such combinations: one with HiLog [34] and one with Transaction Logic [21, 22, 23] Another possible candidate is Annotated Predicate Logic [20, 56, 57], which is a logic for reasoning with inconsistent and uncertain information. This extensibility places F logic in the center of a powerful unifying formalism for reasoning about data and knowledge. This paper is organized as follows. Section 2 discusses the relationship between the ....

....and renders it a suitable basis for developing a theory of object oriented logic programming. F logic is also an extensible logic, as it can be combined with other recently proposed logics for knowledge representation, such as HiLog [34] Transaction Logic [21] and Annotated Predicate Logic [20, 56, 57]. Two such combinations were sketched in Section 17. This extensibility puts F logic in the center of an emerging unified logical formalism for knowledge and data representation. Acknowledgments: We are indebted to Catriel Beeri for his very detailed comments whose length rivals the length of ....

M. Kifer and E.L. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 9(2):179--215, November 1992.

No context found.

M. Kifer and E. L. Lozinskii, "A logic for reasoning with inconsistency," Journal of Automated Reasoning 9(2), pp.179--215, 1992.

No context found.

Kifer, M.; Lozinskii, E.L.: A Logic for Reasoning with Inconsistency. Journal of Automated Reasoning 9:179--215, 1992.

No context found.

M. Kifer and L. Lozinskii E. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 9:179--215, 1992.

No context found.

M. Kifer and E. Lozinskii. A logic for reasoning with inconsistency. Journal of Automated Reasoning, 8:179--215, 1992.

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