Przymusinska, H. and Przymusinski, T. 1990. Semantic Issues in Deductive Databases and Logic Programs. In Formal Techniques in Arti cial Intelligence: a Source-Book, R. Banerji, Ed. North Holland, 321-367.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....on that the above construction introduces at each step exactly the same true and false atoms as the in nite valued approach. ut 6 Related Work The research area of negation in logic programming is very broad and many di erent approaches have been proposed (comprehensive surveys include [1, 9, 4]) In this section we give a brief overview of some of the most generally accepted results and discuss how they relate to the in nite valued approach. The strati ed semantics [2] is one of the rst widely accepted approaches to negation. Informally speaking, a program is strati ed if it does ....

H. Przymusinska and T. Przymusinski. Semantic Issues in Deductive Databases and Logic Programs. In R. Banerji, editor, Formal Techniques in Arti cial Intelligence, pages 321-367. North Holland, 1990.

....structure of the logic programs under consideration, some other 2 valued and 3 valued xpoint semantics are uniquely Such formulae are also called de nite clauses. Figure 1. Belnap four valued structure, FOUR determined. For instance, as shown in [40,41], every standard logic program that is weakly strati ed [40] has a unique weakly perfect model [40] which coincides with its unique stable model [26] and its unique well founded model [47] When negations may also appear in the clause heads, the logic programs may be inconsistent, and so unless ....

H.Przymusinska and T.Przymusinski, Semantic issues in deductive databases and logic programs, in: Formal Techniques in Arti cial Intelligence, ed. R.B.Banej  i, Elsevier Science Publishers, 1990, pp. 321-367.

....But as the reasoning patterns defy one of the fundamental properties of classical logical reasoning, such a characterization is not straightforward to devise. In the case of logic programs this has resulted in a large number of competing proposals. For example, Przymusinska and Przymusinski [114] and Bidoit [7] offer surveys of the various approaches. An obvious approach to characterizing nonmonotonic reasoning declaratively is to devise a suitable logical calculus that captures the correct reasoning patterns. It seems that classical logical calculi are insufficient for the purpose ....

....and Doyle style logics in the stratified case. 7.4 Logic Programs and Deductive Databases The declarative semantics of logic programs and deductive databases has been investigated intensively during the last years and several approaches have been introduced. Przymusinska and Przymusinski [114] and Bidoit [7] present surveys of the field. We consider extended logic programs which are sets of rules of the form l 0 l 1 ; l m ; not l m 1 ; not l n (7:39) where not is the negation as failure operator, n m 0 and each l i is a literal, i.e. an atomic formula or a ....

H. Przymusinska and T.C. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Artificial Intelligence, pages 321--367. North-Holland, Amsterdam, 1990.

....extract more information from our programs. Operator C A P maps partial interpretations to interpretations. We now de ne a new operator which maps partial interpretations to partial interpretations, given what is known to be true and to be false, in the same spirit of Przymusinski s operator [19]: 4 Mark well this is an interpretation, not a partial interpretation De nition 13 (Partial Consequences Operator) Let P be an antitonic logic program, and the two partial interpretations I and J . The partial consequences operator is given by the equation: A P (I ; J) C A P I t ....

H. Przymusinska and T. C. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Articial Intelligence, a Sourcebook, pages 321-367. North Holland, 1990.

....local statification for a broad class of temporal logic programs. Keywords: Temporal Logic Programming, Negation, Stratification, Programming Languages, Deductive Databases. 1 Introduction One of the most interesting and profound research topics in logic programming, is the study of negation [PP90, AB94]. However, most of the research results in this area concern classical logic programming languages. Recent research [Ron01] undertakes the study of stratified negation in temporal logic programming. In this paper, we extend the results obtained in [Ron01] to cover a broader class of temporal logic ....

....Extended Cycle Sum Test In the following, we demonstrate that a Chronolog program accepted by the extended cycle sum test is locally stratified. The following definitions are required (notice that these definitions are the temporal analogs of the corresponding ones for classical logic programs [PP90]) Definition 4.1. Let P be a Chronolog program. The dependency graph DGP of P is a graph whose vertex set is the temporal Herbrand base BP of P and whose edges are determined as follows: if A and B are two atoms in BP , there exists a directed edge from A to B if and only if there exists a ....

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H. Przymusinska and T. Przymusinski. Semantic issues in deductive databases and logic programming. In R. Banerji, editor, Formal Techniques in Arrtificial Intelligence, pages 321--367. North Holland, 1990.

....to the sets of abductive hypotheses and the abductive procedure introduced in [4] 2 Preliminary De nitions and Observations In the rest of this paper we will consider general programs, i.e. Horn clause programs with negation. As base reference for semantics of general logic programs we take [15], which is entirely devoted to a systematic exposition and comparison of the various proposed semantics. As a base reference for semantics of positive logic programs we take [13] Clauses in a general program have an atom as conclusion, and a conjunction of literals as conditions, where a literal ....

....literal in the conditions of a clause in P . Negation is indicated with not. By interpretations and models we mean Herbrand interpretations and Herbrand models respectively. Since an Herbrand interpretation is a model of a program P if and only if it is a model of its ground instantiation [15] (Cor. 4.1) we will assume, without further mention (and as it is customary in the literature) that every program P has already been instantiated. That is, by P we mean the (possibly in nite) propositional theory consisting of all ground instances of clauses from P . By H P and B P we indicate ....

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H. Przymusinska and T. Przymusinski. Semantic Issues in Deductive Databases and Logic Programs. R.B. Banerji (ed.) Formal Techniques in Articial Intelligence, a Sourcebook, Elsevier Science Publisher B.V. (North Holland), 1990.

....considerable research attention largely due to its applications in areas such as artificial intelligence and deductive databases. From a semantic point of view, the addition of negation in classical logic programming is far from straightforward and many different approaches have been developed [PP90, AB94]. One of the earliest such approaches is the so called stratified negation [ABW88] Intuitively, a stratified logic program is one in which negation is not used in a circular way, and this (syntactically determinable) condition ensures that the program has a unique perfect model. Stratification ....

....on the cycle sum test is necessary. There is an important difference between the test described above and the usual stratification tests for classical logic programming. Given a classical logic program with negation, a stratification algorithm usually constructs a program dependency graph [PP90] and the edges of the graph are labeled as positive or negative depending on whether they connect the head of a program clause with a positive or negative literal in the body of the clause. The cycle sum test as defined above, does not take into consideration positive and negative edges, and it ....

[Article contains additional citation context not shown here]

H. Przymusinska and T. Przymusinski. Semantic Issues in Deductive Databases and Logic Programs. In R. Banerji, editor, Formal Techniques in Artificial Intelligence, pages 321--367. North Holland, 1990.

.... semantics for logic programs see [13, 14, 15, 16, 18] cf. also [35] In addition, a number of approaches have appeared that partly overcome the above problem by grounding a reasoning about logic programs and (some of) their semantics on various logical formalisms, be it three valued logic [30], intuitionistic logic [29] a general theory of argumentation [19] or a modal logic [32] In this study we will show that there exists a logical interpretation of program clauses of a most general kind that agrees with the majority of their procedural interpretations. In our framework, such ....

H. Przymusinska and T. Przymusinski (1990) Semantic issues in deductive databases and logic programs, in R. Benerji (ed.) Formal Techniques in Articial Intelligence, North-Holland: Amsterdam, pp. 321-367.

....Section 4 contains the definitions based on methods from non monotonic reasoning. We compare their expressiveness and show that they satisfy natural closure properties. We assume the reader has knowledge of standard terminology and definitions in logic programming as found in, for example, [14, 22]. Results claimed in this abstract are proved in a fuller version of this paper. 2 Rational Trees We begin by defining the rational trees as a subset of the infinite trees. Then we discuss the use of rational trees to represent pointer based data structures. Let Sigma be the set of function ....

H. Przymusinska & T. Przymusinski, Semantic Issues in Deductive Databases and Logic Programs, in: Sourcebook on the Formal Approaches in Artificial Intelligence, A. Banerji (Ed.), North-Holland, to appear.

....In section 5 we present our results, showing for which semantics and transformations equivalence is preserved. Proofs have been omitted. 2 Preliminaries Due to space limitations, only a sketchy development of preliminary definitions is given. Further details can be obtained from [16] 9] 13] [18]. We assume throughout that there is an intended domain of computation D. The structure D defines the set D of elements over which computation will be performed and defines the functions and constraints. The class of constraints is closed under conjunction. A valuation v maps terms to D. We call ....

....f:a; bg. One further useful case when the translation property does hold between semantics is when one semantics is a restriction of the other. Application of the following proposition shows that the translation property holds between 3 valued stable semantics and the well founded semantics (see [18]) Proposition 1 If, for every program P , S 2 (P ) fM j M 2 S 1 (P ) C(M;S 1 (P ) g for some condition C depending only on M and S 1 (P ) then the translation property holds between S 1 and S 2 . Proof: Suppose S 1 (P ) S 1 (P 0 ) Then C(M;S 1 (P ) iff C(M;S 1 (P 0 ) Thus S ....

H. Przymusinska & T. Przymusinski, Semantic Issues in Deductive Databases and Logic Programs, in: Sourcebook on the Formal Approaches in Artificial Intelligence, A. Banerji (Ed.), North-Holland, to appear.

....with respect to this semantics. Later, negation as failure was shown to be complete on some classes of programs. Other notions of negation have been intended for deductive databases (function free logic programs) or derived from an aim of common sense or non monotonic reasoning (see [37] for a survey) Although the logical semantics of these approaches is elegant, they are not computationally feasible when function symbols are allowed in programs. Indeed, these semantics are uncomputable, in general. In this section we look at a notion of negation called constructive negation . ....

H. Przymusinska & T. Przymusinski, Semantic Issues in Deductive Databases and Logic Programs, in: Sourcebook on the Formal Approaches in Artificial Intelligence, A. Banerji (Ed.), North-Holland, to appear.

.... Sakama dropped the C scheme in his Extended Well Founded Semantics [50] thereby obtaining a paraconsistent version of WFS for extended logic programs (EWFS) The original presentation of his semantics is based on Przymuskinski s constructive definition of WFS in terms of the Theta operator [45]. We prefer the following more declarative and simpler definition, which is equivalent to the one in [50] and supercedes the one of Definition 2. Definition 20. Let P be an extended logic program. The extended well founded model MP of the program is obtained as follows: 1. Transform program P ....

....a is an arbitrary atom. It is immediately recognizable that an XDB X is well founded iff P l is acyclic [4] and weakly well founded iff P l is locally stratified [46] Therefore P l is locally stratified and has a unique perfect model which is equivalent to the well founded model of P l [45]. It is not difficult to see that the following correspondence holds: Theorem 32. Let X be a weakly well founded XDB. Then the following equivalences hold, where a is an atom in the language of X: MX j= a iff a p 2 WFM(P l ) MX j= Gammaa iff not a p 2 WFM(P l ) MX j= a iff a n 2 ....

[Article contains additional citation context not shown here]

H. Przymusinska and T. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Artificial Intelligence, a Sourcebook, pages 321--367. North Holland, 1990.

....Accordingly, the WFSX of P is f:a; b; not a; not :bg, since b follows from not a. The formal definition of this semantics is made by embedding that requirement into the very definition of (3 valued) interpretation, and then by straightforwardly adapting to it the formal techniques used for WFS in [16]. Since this semantics exhibits all the above mentioned properties of strong negation and is defined as an extension of WFS, it seems that it should be closely related to stationary semantics with strong negation. In fact: Theorem 4.4 (WFSX Semantics and Strong Negation) If an interpretation M ....

....shown with the help of an example. Example 10 Consider the program P = fa not a; b a; b g; which has no strong stationary models. According to WFSX its well founded model (and only extended stable model) is M = f:b; not b; not :ag: Note that M is not even a model in the (usual) sense of [16], because for the second rule the truth value of the head (false) is smaller than the truth value of the body (undefined) In [11] a new truth valuation function is defined that agrees with the required definition of extended stable models. The main difference between this and the truth valuation ....

[Article contains additional citation context not shown here]

H. Przymusinska and T. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Artificial Intelligence. North Holland, 1990.

....But as the reasoning patterns defy one of the fundamental properties of classical logical reasoning, such a characterization is not straightforward to devise. In the case of logic programs this has resulted in a large number of competing proposals. For example, Przymusinska and Przymusinski [95] and Bidoit [9] ooeer surveys of the various approaches. An obvious approach to characterizing nonmonotonic reasoning declaratively is to devise a suitable logical calculus that captures the correct reasoning patterns. A large number of researchers have studied the formal underpinnings of ....

H. Przymusinska and T.C. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Articial Intelligence, pages 321367. North-Holland, Amsterdam, 1990.

....Practical implementations of logic programming such as PROLOG are general programming tools and in wide use nowadays. Sterling and Shapiro [ 1986 ] discuss logic programming methodology at large in their book iThe Art of PROLOGj. Logic programming has a close connection to deductive databases [ Przymusinska and Przymusinski, 1990 ] Deductive databases can store and manipulate deductive rules of reasoning (intensional data) in addition to storing individual facts (extensional data) Logic programs can be seen as deductive databases: the unit clauses of a logic program form the extensional data and the rest of the clauses ....

....logic. Przymusinski has extensively studied the relationship between the well founded semantics of logic programs and 3 valued autoepistemic logic [ Przymusinski, 1989; Przymusinski, 1991b; Przymusinski, 1991a ] Inheritance reasoning can be captured in autoepistemic logic [ Gelfond and Przymusinska, 1990 ] Kakas and Mancarella [ 1990 ] embed abduction into autoepistemic logic. Elkan [ 1990 ] gives a translation from truth maintenance systems. This interconnection has also been studied in [ Reinfrank et al. 1989 ] and [ Fujiwara and S. 1989 ] Since these concrete translations exist, the ....

H. Przymusinska and T.C. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Articial Intelligence, pages 321 367. North-Holland, Amsterdam, 1990.

....[ Przymusinski, 1988 ] of stratied logic programs coincides with the xpoint construction, as do the stable model semantics and well founded semantics. Hence all major semantics agree on the meaning of stratied programs. A good discussion of this subject and the above semantics can be found in [ Przymusinska and Przymusinski, 1990 ] Stratication conditions for nonmonotonic logics based on the similar concept for logic programs have been presented e.g. in [ Bidoit and Froidevaux, 1991; Gelfond, 1987; Marek and Truszczy#ski, 1991 ] The denitions of stratication for autoepistemic logic and some of the denitions for ....

H. Przymusinska and T. C. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Articial Intelligence, pages 321 367. North-Holland, Amsterdam, 1990.

....in these logic programs is, however, rather limited since their semantics suggested in [Min82] is closely related to the notion of minimal model and implicitly assumes a form of the closed world assumption. This work was generalized and or modified by various authors (an overview can be found in [PP90a], LMR92] but most of the approaches still assume the closed world assumption, and hence do not allow the representation of such simple forms of incompleteness as missing information in the database tables, null values and partial definitions. In this section, we discuss another approach to ....

H. Przymusinska and T. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Manerji, editor, Formal Techniques in Artificial Intelligence, pages 321 -- 367. North Holland, Amsterdam, 1990.

....formalism on which the meaning of negation by default not is based and a suitable method of defining the semantics using this default formalism. Both problems turned out to be difficult and a significant number of recent papers have been recently devoted to the study of this important problem [ABW88, Prz88, VGRS90, GL88, PP90]. We propose here a formalization which specifies the meaning of negation by default not C by the following natural condition: not C j C is false in all minimal models which says that negation of C can be assumed by default if and only if C is false in all minimal models of the theory. In other ....

H. Przymusinska and T. C. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Artificial Intelligence, pages 321--367. NorthHolland, Amsterdam, 1990.

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Przymusinska, H. and Przymusinski, T. 1990. Semantic Issues in Deductive Databases and Logic Programs. In Formal Techniques in Arti cial Intelligence: a Source-Book, R. Banerji, Ed. North Holland, 321-367.

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H. Przymusinska and T. Przymusinski. Semantic Issues in Deductive Databases and Logic Programs. In R. Banerji, editor, Formal Techniques in Arti cial Intelligence, pages 321-367. North Holland, 1990.

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H. Przymusinska and T. C. Przymusinski, Semantic Issues in Deductive Databases and Logic Programs, R.B. Banerji (ed.) Formal Techniques in Artificial Intelligence, a Sourcebook: Elsevier Sc. Publ. B.V. (North Holland), 1990.

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H. Przymusinska and T. C. Przymusinski, Semantic Issues in Deductive Databases and Logic Programs, R.B. Banerji (ed.) Formal Techniques in Artificial Intelligence, a Sourcebook: Elsevier Sc. Publ. B.V. (North Holland), 1990.

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H. Przymusinska and T. C. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Arti cial Intelligence, a Sourcebook, pages 321-367. North Holland, 1990.

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H. Przymusinska and T. C. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Arti cial Intelligence, a Sourcebook, pages 321-367. North Holland, 1990.

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H. Przymusinska and T. C. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Artificial Intelligence, a Sourcebook, pages 321--367. North Holland, 1990.

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