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Functional Stable Model Semantics and Answer Set Programming Modulo Theories
 PROCEEDINGS OF THE TWENTYTHIRD INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2013
"... Recently there has been an increasing interest in incorporating “intensional” functions in answer set programming. Intensional functions are those whose values can be described by other functions and predicates, rather than being predefined as in the standard answer set programming. We demonstrate t ..."
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Recently there has been an increasing interest in incorporating “intensional” functions in answer set programming. Intensional functions are those whose values can be described by other functions and predicates, rather than being predefined as in the standard answer set programming. We demonstrate that the functional stable model semantics plays an important role in the framework of “Answer Set Programming Modulo Theories (ASPMT)” —a tight integration of answer set programming and satisfiability modulo theories, under which existing integration approaches can be viewed as special cases where the role of functions is limited. We show that “tight” ASPMT programs can be translated into SMT instances, which is similar to the known relationship between ASP and SAT.
Interpolable Formulas in Equilibrium Logic and Answer Set Programming
"... Interpolation is an important property of classical and many nonclassical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the nonmonotonic system of equilibrium logic, establishing weaker or stronger forms of ..."
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Interpolation is an important property of classical and many nonclassical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the nonmonotonic system of equilibrium logic, establishing weaker or stronger forms of interpolation depending on the precise interpretation of the inference relation. These results also yield a form of interpolation for ground logic programs under the answer sets semantics. For disjunctive logic programs we also study the property of uniform interpolation that is closely related to the concept of variable forgetting. The firstorder version of equilibrium logic has analogous Interpolation properties whenever the collection of equilibrium models is (firstorder) definable. Since this is the case for socalled safe programs and theories, it applies to the usual situations that arise in practical answer set programming. 1.
Mathematical logic for life science ontologies
 DE QUEIROZ (EDS.), LOGIC, LANGUAGE, INFORMATION AND COMPUTATION, 16TH INT. WORKSHOP, WOLLIC 2009
, 2009
"... We discuss how concepts and methods introduced in mathematical logic can be used to support the engineering and deployment of life science ontologies. The required applications of mathematical logic are not straighforward and we argue that such ontologies provide a new and rich family of logical th ..."
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We discuss how concepts and methods introduced in mathematical logic can be used to support the engineering and deployment of life science ontologies. The required applications of mathematical logic are not straighforward and we argue that such ontologies provide a new and rich family of logical theories that wait to be explored by logicians.
Forgetting in logic programs under strong equivalence
 In Principles of Knowledge Representation and Reasoning: Proceedings of the Thirteenth International Conference
, 2012
"... Abstract In this paper, we propose a semantic forgetting for arbitrary logic programs (or propositional theories) under answer set semantics, called HTforgetting. The HTforgetting preserves strong equivalence in the sense that strongly equivalent logic programs will remain strongly equivalent afte ..."
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Abstract In this paper, we propose a semantic forgetting for arbitrary logic programs (or propositional theories) under answer set semantics, called HTforgetting. The HTforgetting preserves strong equivalence in the sense that strongly equivalent logic programs will remain strongly equivalent after forgetting the same set of atoms. The result of an HTforgetting is always expressible by a logic program, and in particular, the result of an HTforgetting in a Horn program is expressible in a Horn program; and a representation theorem shows that HTforgetting can be precisely characterized by ZhangZhou's four forgetting postulates under the logic of hereandthere. We also reveal underlying connections between HTforgetting and classical forgetting, and provide complexity results for decision problems.
Forgetting for Answer Set Programs Revisited
 PROCEEDINGS OF THE TWENTYTHIRD INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... A new semantic forgetting for answer set programs (ASP), called SMforgetting, is proposed in the paper. It distinguishes itself from the others in that it preserves not only skeptical and credulous consequences on unforgotten variables, but also strong equivalence – forgetting same variables in str ..."
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A new semantic forgetting for answer set programs (ASP), called SMforgetting, is proposed in the paper. It distinguishes itself from the others in that it preserves not only skeptical and credulous consequences on unforgotten variables, but also strong equivalence – forgetting same variables in strongly equivalent logic programs has strongly equivalent results. The forgetting presents a positive answer to Gabbay, Pearce and Valverde’s open question – if ASP has uniform interpolation property. We also investigate some properties, algorithm and computational complexities for the forgetting. It shows that computing the forgetting result is generally intractable even for Horn logic programs.
Forgetting for Knowledge Bases in DLLitebool
 In Proc. ARCOE’09 (IJCAI’09 Workshop
, 2009
"... We address the problem of term elimination in DLLite ontologies by adopting techniques from classical forgetting theory. Specifically, we generalize our previous results on forgetting in DLLitecore TBox to forgetting in DLLitebool KBs. We also introduce querybased forgetting, a parameterized de ..."
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We address the problem of term elimination in DLLite ontologies by adopting techniques from classical forgetting theory. Specifically, we generalize our previous results on forgetting in DLLitecore TBox to forgetting in DLLitebool KBs. We also introduce querybased forgetting, a parameterized definition of forgetting, which provides a unifying framework for defining and comparing different definitions of forgetting in DLLite ontologies. 1
Uniform Interpolation for ALC Revisited
"... The notion of uniform interpolation for description logic ALC has been ..."
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The notion of uniform interpolation for description logic ALC has been
A SyntaxIndependent Approach to Forgetting in Disjunctive Logic Programs
"... In this paper, we present an approach to forgetting in disjunctive logic programs, where forgetting an atom from a program amounts to a reduction in the signature of that program. Notably, the approach is syntaxindependent, so that if two programs are strongly equivalent, then the result of forge ..."
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In this paper, we present an approach to forgetting in disjunctive logic programs, where forgetting an atom from a program amounts to a reduction in the signature of that program. Notably, the approach is syntaxindependent, so that if two programs are strongly equivalent, then the result of forgetting a given atom in each program is also strongly equivalent. Our central definition of forgetting is abstract: forgetting an atom from program P is characterised by the set of those SE consequences of P that do not mention the atom to be forgotten. We provide an equivalent, syntactic, characterization in which forgetting an atom p is given by those rules in the program that do not mention p, together with rules obtained by a single inference step from those rules that do mention p. Forgetting is shown to have appropriate properties; in particular, answer sets are preserved in forgetting an atom. As well, forgetting an atom via the syntactic characterization results in a modest (at worst quadratic) blowup in the program size. Finally, we provide a prototype implementation of this approach to forgetting.
Eliminating concepts and roles from ontologies in expressive descriptive logics.
 COMPUTATIONAL INTELLIGENCE 30(2):205–232
"... Forgetting is an important tool for reducing ontologies by eliminating some redundant concepts and roles while preserving sound and complete reasoning. Attempts have previously been made to address the problem of forgetting in relatively simple description logics (DLs) such as DLLite and extended E ..."
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Forgetting is an important tool for reducing ontologies by eliminating some redundant concepts and roles while preserving sound and complete reasoning. Attempts have previously been made to address the problem of forgetting in relatively simple description logics (DLs) such as DLLite and extended EL. However, the issue of forgetting for ontologies in more expressive description logics, such as ALC and OWL DL, is largely unexplored. In particular, the problem of characterizing and computing forgetting for such logics is still open. In this paper, we first define semantic forgetting about concepts and roles in ALC ontologies and state several important properties of forgetting in this setting. We then define the result of forgetting for concept descriptions in ALC, state the properties of forgetting for concept descriptions, and present algorithms for computing the result of forgetting for concept descriptions. Unlike the case of DLLite, the result of forgetting for an ALC ontology does not exist in general, even for the special case of forgetting in TBoxes. This makes the problem of how to compute forgetting in ALC more challenging. We address this problem by defining a series of approximations to the result of forgetting for ALC ontologies and studying their properties and their application to reasoning tasks. We use the algorithms for computing forgetting for concept descriptions to compute these approximations. Our algorithms for computing approximations can be embedded into an ontology editor to enhance its ability to manage and reason in (large) ontologies.
Variable forgetting in reasoning about knowledge.
 JAIR
, 2009
"... Abstract In this paper, we investigate knowledge reasoning within a simple framework called knowledge structure. We use variable forgetting as a basic operation for one agent to reason about its own or other agents' knowledge. In our framework, two notions namely agents' observable variab ..."
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Abstract In this paper, we investigate knowledge reasoning within a simple framework called knowledge structure. We use variable forgetting as a basic operation for one agent to reason about its own or other agents' knowledge. In our framework, two notions namely agents' observable variables and the weakest sufficient condition play important roles in knowledge reasoning. Given a background knowledge base Γ and a set of observable variables O i for each agent i, we show that the notion of agent i knowing a formula ϕ can be defined as a weakest sufficient condition of ϕ over O i under Γ. Moreover, we show how to capture the notion of common knowledge by using a generalized notion of weakest sufficient condition. Also, we show that public announcement operator can be conveniently dealt with via our notion of knowledge structure. Further, we explore the computational complexity of the problem whether an epistemic formula is realized in a knowledge structure. In the general case, this problem is PSPACEhard; however, for some interesting subcases, it can be reduced to coNP. Finally, we discuss possible applications of our framework in some interesting domains such as the automated analysis of the wellknown muddy children puzzle and the verification of the revised NeedhamSchroeder protocol. We believe that there are many scenarios where the natural presentation of the available information about knowledge is under the form of a knowledge structure. What makes it valuable compared with the corresponding multiagent S5 Kripke structure is that it can be much more succinct.