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Introspective forgetting
, 2009
"... We model the forgetting of propositional variables in a modal logical context where agents become ignorant and are aware of each others ’ or their own resulting ignorance. The resulting logic is sound and complete. It can be compared to variableforgetting as abstraction from information, wherein ..."
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We model the forgetting of propositional variables in a modal logical context where agents become ignorant and are aware of each others ’ or their own resulting ignorance. The resulting logic is sound and complete. It can be compared to variableforgetting as abstraction from information, wherein agents become unaware of certain variables: by employing elementary results for bisimulation, it follows that beliefs not involving the forgotten atom(s) remain true.
Forgetting for Defeasible Logic
"... Abstract. The concept of forgetting has received significant interest in artificial intelligence recently. Informally, given a knowledge base, we may wish to forget about (or discard) some redundant parts (such as atoms, predicates, concepts, etc) but still preserve the consequences for certain form ..."
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Abstract. The concept of forgetting has received significant interest in artificial intelligence recently. Informally, given a knowledge base, we may wish to forget about (or discard) some redundant parts (such as atoms, predicates, concepts, etc) but still preserve the consequences for certain forms of reasoning. In nonmonotonic reasoning, so far forgetting has been studied only in the context of extension based approaches, mainly answerset programming. In this paper forgetting is studied in the context of defeasible logic, which is a simple, efficient and sceptical nonmonotonic reasoning approach. 1
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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Cited by 3 (3 self)
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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.
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.
K.: Forgetting under the wellfounded semantics
 Logic Programming and Nonmonotonic Reasoning, 12th International Conference, LPNMR 2013, Corunna
"... Abstract. In this paper, we develop a notion of forgetting for normal logic programs under the wellfounded semantics. We show that a number of desirable properties are satisfied by our approach. Three different algorithms are presented that maintain the computational complexity of the wellfounded ..."
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Abstract. In this paper, we develop a notion of forgetting for normal logic programs under the wellfounded semantics. We show that a number of desirable properties are satisfied by our approach. Three different algorithms are presented that maintain the computational complexity of the wellfounded semantics, while partly keeping its syntactical structure. 1
Quantitatively Evaluating FormulaVariable Relevance by Forgetting
"... Abstract. Forgetting is a feasible tool for weakening knowledge bases by focusing on the most important issues, and ignoring irrelevant, outdated, or even inconsistent information, in order to improve the efficiency of inference, as well as resolve conflicts in the knowledge base. Also, forgetting h ..."
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Abstract. Forgetting is a feasible tool for weakening knowledge bases by focusing on the most important issues, and ignoring irrelevant, outdated, or even inconsistent information, in order to improve the efficiency of inference, as well as resolve conflicts in the knowledge base. Also, forgetting has connections with relevance between a variable and a formula. However, in the existing literature, the definition of relevance is “binary ” – there are only the concepts of “relevant ” and “irrelevant”, and no means to evaluate the “degree ” of relevance between variables and formulas. This paper presents a method to define the formulavariable relevance in a quantitative way, using the tool of variable forgetting, by evaluating the change of model set of a certain formula after forgetting a certain variable in it. We also discuss properties, examples and one possible application of the definition.
IRITCNRS, Toulouse
"... We present and study a general family of belief update operators in a propositional setting. Its operators are based on formula/literal dependence, which is more finegrained than the notion of formula/variable dependence that was proposed in the literature: formula/variable dependence is a particul ..."
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We present and study a general family of belief update operators in a propositional setting. Its operators are based on formula/literal dependence, which is more finegrained than the notion of formula/variable dependence that was proposed in the literature: formula/variable dependence is a particular case of formula/literal dependence. Our update operators are defined according to the “forgetthenconjoin ” scheme: updating a belief base by an input formula consists in first forgetting in the base every literal on which the input formula has a negative influence, and then conjoining the resulting base with the input formula. The operators of our family differ by the underlying notion of formula/literal dependence, which may be defined syntactically or semantically, and which may or may not exploit further information like known persistent literals and preset dependencies. We argue that this allows to handle the frame problem and the ramification problem in a more appropriate way. We evaluate the update operators of our family w.r.t. two important dimensions: the logical dimension, by checking the status of the KatsunoMendelzon postulates for update, and the computational dimension, by identifying the complexity of a number of decision problems (including model checking, consistency and inference), both in the general case and in some restricted cases, as well as by studying compactability issues. It follows that
On Forgetting Postulates in Answer Set Programming
"... Forgetting is an important mechanism for logicbased agent systems. A recent interest has been in the desirable properties of forgetting in answer set programming (ASP) and their impact on the design of forgetting operators. It is known that some subsets of these properties are incompatible, i.e., ..."
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Forgetting is an important mechanism for logicbased agent systems. A recent interest has been in the desirable properties of forgetting in answer set programming (ASP) and their impact on the design of forgetting operators. It is known that some subsets of these properties are incompatible, i.e., they cannot be satisfied at the same time. In this paper, we are interested in the question on the largest set ∆ of pairs (Π, V), where Π is a logic program and V is a set of atoms, such that a forgetting operator exists that satisfies all the desirable properties for each (Π, V) in ∆. We answer this question positively by discovering the precise condition under which the knowledge forgetting, a wellestablished approach to forgetting in ASP, satisfies the property of strong persistence, which leads to a sufficient and necessary condition for a forgetting operator to satisfy all the desirable properties proposed in the literature. We explore computational complexities on checking the condition and present a syntactic characterization which can serve as the basis of computing knowledge forgetting in ASP.