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 ....

[Article contains additional citation context not shown here]

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 ....

[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, 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 ....

[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.

....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.

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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.

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.

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

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