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51
Explicit Provability And Constructive Semantics
 Bulletin of Symbolic Logic
, 2001
"... In 1933 G odel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that G odel's provability calculus is nothing b ..."
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Cited by 114 (22 self)
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In 1933 G odel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that G odel's provability calculus is nothing but the forgetful projection of LP. This also achieves G odel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a BrouwerHeytingKolmogorov style provability semantics for Int which resisted formalization since the early 1930s. LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and #calculus.
A New Logical Characterisation of Stable Models and Answer Sets
 In Proc. of NMELP 96, LNCS 1216
, 1997
"... This paper relates inference in extended logic programming with nonclassical, nonmonotonic logics. We define a nonmonotonic logic, called equilibrium logic, based on the least constructive extension, N2, of the intermediate logic of "hereandthere". We show that on logic programs equilibrium logic ..."
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Cited by 44 (11 self)
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This paper relates inference in extended logic programming with nonclassical, nonmonotonic logics. We define a nonmonotonic logic, called equilibrium logic, based on the least constructive extension, N2, of the intermediate logic of "hereandthere". We show that on logic programs equilibrium logic coincides with the inference operation associated with the stable model and answer set semantics of Gelfond and Lifschitz. We thereby obtain a very simple characterisation of answer set semantics as a form of minimal model reasoning in N2, while equilibrium logic itself provides a natural generalisation of this semantics to arbitrary theories. We discuss briefly some consequences and applications of this result. 1 Introduction By contrast with the minimal model style of reasoning characteristic of several approaches to the semantics of logic programs, the stable model semantics of Gelfond and Lifschitz [8] was, from the outset, much closer in spirit to the styles of reasoning found in othe...
Revision Programming
 THEORETICAL COMPUTER SCIENCE
, 1994
"... In this paper we introduce revision programming  a logicbased framework for describing constraints on databases and providing a computational mechanism to enforce them. Revision programming captures those constraints that can be stated in terms of the membership (presence or absence) of items (re ..."
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Cited by 36 (1 self)
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In this paper we introduce revision programming  a logicbased framework for describing constraints on databases and providing a computational mechanism to enforce them. Revision programming captures those constraints that can be stated in terms of the membership (presence or absence) of items (records) in a database. Each such constraint is represented by a revision rule ff / ff 1 ; : : : ; ff k , where ff and all ff i are of the form in(a) and out(b). Collections of revision rules form revision programs. Similarly as logic programs, revision programs admit both declarative and imperative (procedural) interpretations. In our paper, we introduce a semantics that reflects both interpretations. Given a revision program, this semantics assigns to any database B a collection (possibly empty) of Pjustified revisions of B. The paper contains a thorough study of revision programming. We exhibit several fundamental properties of revision programming. We study the relationship of revision programming to logic programming. We investigate complexity of reasoning with revision programs as well as algorithms to compute P justified revisions. Most importantly from the practical database perspective, we identify two classes of revision programs, safe and stratified, with a desirable property that they determine for each initial database a unique revision.
Twelve Definitions of a Stable Model
"... This is a review of some of the definitions of the concept of a stable model that have been proposed in the literature. These definitions are equivalent to each other, at least when applied to traditional Prologstyle programs, but there are reasons why each of them is valuable and interesting. A n ..."
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Cited by 19 (1 self)
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This is a review of some of the definitions of the concept of a stable model that have been proposed in the literature. These definitions are equivalent to each other, at least when applied to traditional Prologstyle programs, but there are reasons why each of them is valuable and interesting. A new characterization of stable models can suggest an alternative picture of the intuitive meaning of logic programs; or it can lead to new algorithms for generating stable models; or it can work better than others when we turn to generalizations of the traditional syntax that are important from the perspective of answer set programming; or it can be more convenient for use in proofs; or it can be interesting simply because it demonstrates a relationship between seemingly unrelated ideas.
Reducts of propositional theories, satisfiability relations, and generalizations of semantics of logic programs
"... Abstract. Over the years, the stablemodel semantics has gained a position of the correct (twovalued) interpretation of default negation in programs. However, for programs with aggregates (constraints), the stablemodel semantics, in its broadly accepted generalization stemming from the work by Pea ..."
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Cited by 11 (0 self)
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Abstract. Over the years, the stablemodel semantics has gained a position of the correct (twovalued) interpretation of default negation in programs. However, for programs with aggregates (constraints), the stablemodel semantics, in its broadly accepted generalization stemming from the work by Pearce, Ferraris and Lifschitz, has a competitor: the semantics proposed by Faber, Leone and Pfeifer, which seems to be essentially different. Our goal is to explain the relationship between the two semantics. Pearce, Ferraris and Lifschitz’s extension of the stablemodel semantics is best viewed in the setting of arbitrary propositional theories. We propose here an extension of the FaberLeonePfeifer semantics, or FLP semantics, for short, to the full propositional language, which reveals both common threads and differences between the FLP and stablemodel semantics. We use our characterizations of FLPstable models to derive corresponding results on strong equivalence and on normal forms of theories under the FLP semantics. We apply a similar approach to define supported models for arbitrary propositional theories, and to study their properties. 1
Weight Constraints as Nested Expressions
 In
, 2000
"... We compare two recent extensions of the answer set (stable model) semantics of logic programs. One of them, due to Lifschitz, Tang and Turner, allows the bodies and heads of rules to contain nested expressions. The other, due to Niemela and Simons, uses weight constraints. We show that there is ..."
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Cited by 8 (1 self)
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We compare two recent extensions of the answer set (stable model) semantics of logic programs. One of them, due to Lifschitz, Tang and Turner, allows the bodies and heads of rules to contain nested expressions. The other, due to Niemela and Simons, uses weight constraints. We show that there is a simple, modular translation from the language of weight constraints into the language of nested expressions that preserves the program's answer sets. This translation can be used to study equivalent transformations of logic programs written in the input language of the answer set programming system SMODELS. Keywords: answer sets, cardinality constraints, SMODELS, stable models, weight constraints. 1
Logic Programming for Knowledge Representation
, 2007
"... This note provides background information and references to the tutorial on recent research developments in logic programming inspired by need of knowledge representation. ..."
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Cited by 7 (0 self)
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This note provides background information and references to the tutorial on recent research developments in logic programming inspired by need of knowledge representation.
Reformulating the Situation Calculus and the Event Calculus in the General Theory of Stable Models and in Answer Set Programming
"... Circumscription and logic programs under the stable model semantics are two wellknown nonmonotonic formalisms. The former has served as a basis of classical logic based action formalisms, such as the situation calculus, the event calculus and temporal action logics; the latter has served as a basis ..."
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Cited by 7 (5 self)
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Circumscription and logic programs under the stable model semantics are two wellknown nonmonotonic formalisms. The former has served as a basis of classical logic based action formalisms, such as the situation calculus, the event calculus and temporal action logics; the latter has served as a basis of a family of action languages, such as language A and several of its descendants. Based on the discovery that circumscription and the stable model semantics coincide on a class of canonical formulas, we reformulate the situation calculus and the event calculus in the general theory of stable models. We also present a translation that turns the reformulations further into answer set programs, so that efficient answer set solvers can be applied to compute the situation calculus and the event calculus. 1.
Strongly equivalent temporal logic programs
"... This paper analyses the idea of strong equivalence for transition systems represented as logic programs under the Answer Set Programming (ASP) paradigm. To check strong equivalence, we use a linear temporal extension of Equilibrium Logic (a logical characterisation of ASP) and its monotonic basis, t ..."
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Cited by 6 (3 self)
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This paper analyses the idea of strong equivalence for transition systems represented as logic programs under the Answer Set Programming (ASP) paradigm. To check strong equivalence, we use a linear temporal extension of Equilibrium Logic (a logical characterisation of ASP) and its monotonic basis, the intermediate logic of HereandThere (HT). Trivially, equivalence in this temporal extension of HT provides a sufficient condition for temporal strong equivalence and, as we show in the paper, it can be transformed into a provability test into the standard Linear Temporal Logic (LTL), something that can be automatically checked using any of the LTL available provers. The paper shows an example of the potential utility of this method by detecting some redundant rules in a simple actions reasoning scenario.
Temporal Equilibrium Logic: a first approach ⋆
"... Abstract. In this paper we introduce an extension of Equilibrium Logic (a logical characterisation of the Answer Set Semantics for logic programs) consisting in the inclusion of modal temporal operators, as those used in Linear Temporal Logic. As a result, we obtain a very expressive formalism that ..."
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Cited by 5 (3 self)
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Abstract. In this paper we introduce an extension of Equilibrium Logic (a logical characterisation of the Answer Set Semantics for logic programs) consisting in the inclusion of modal temporal operators, as those used in Linear Temporal Logic. As a result, we obtain a very expressive formalism that allows nonmonotonic reasoning for temporal domains. To show an example of its utility, we present a translation of a language for reasoning about actions into this formalism. 1