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Nonmonotonic Reasoning, Preferential Models and Cumulative Logics
, 1990
"... Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of ..."
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Cited by 538 (13 self)
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Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen [13]. Both prooftheoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay in [10], while the latter has been advocated by Y. Shoham in [38]. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interest, that of preferential relations, turns out to have been studied by E. Adams in [2]. The pr...
Defeasible Logic
 Handbook of Logic in Artificial Intelligence and Logic Programming
, 2001
"... We often reach conclusions partially on the basis that we do not have evidence that the conclusion is false. A newspaper story warning that the local water supply has been contaminated would prevent a person from drinking water from the tap in her home. This suggests that the absence of such evidenc ..."
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Cited by 182 (4 self)
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We often reach conclusions partially on the basis that we do not have evidence that the conclusion is false. A newspaper story warning that the local water supply has been contaminated would prevent a person from drinking water from the tap in her home. This suggests that the absence of such evidence contributes to her usual belief that her water is safe. On the other hand, if a reasonable person received a letter telling her that she had won a million dollars, she would consciously consider whether there was any evidence that the letter was a hoax or somehow misleading before making plans to spend the money. All to often we arrive at conclusions which we later retract when contrary evidence becomes available. The contrary evidence defeats our earlier reasoning. Much of our reasoning is defeasible in this way. Since around 1980, considerable research in AI has focused on how to model reasoning of this sort. In this paper, I describe one theoretical approach to this problem, discuss implementation of this approach as an extension of Prolog, and describe some application of this work to normative reasoning, learning, planning, and other types of automated reasoning.
Logic and Databases: a 20 Year Retrospective
, 1996
"... . At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire ..."
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Cited by 55 (1 self)
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. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...
Inference in DATR
, 1989
"... DATR is a declarative language for representing a restricted class of inheritance networks, permitting both multiple and default inheritance. The principal intended area of application is the representation of lexical entries for natural language processing, and we use examples from this domain thro ..."
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Cited by 48 (4 self)
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DATR is a declarative language for representing a restricted class of inheritance networks, permitting both multiple and default inheritance. The principal intended area of application is the representation of lexical entries for natural language processing, and we use examples from this domain throughout. In this paper we present the syntax and inference mechanisms for the language. The goal of the DATR enterprise is the design of a simple language that (i) has the necessary expressive power to encode the lexical entries presupposed by contemporary work in the unification grammar tradition, (ii) can express all the evident generalizations about such entries, (iii) has an explicit theory of inference, (iv) is computationally tractable, and (v) has an explicit declarative semantics. The present paper is primarily concerned with (iii), though the examples used may hint at our strategy in respect of (i) and (ii).
Uniform Semantic Treatment of Default and Autoepistemic Logics
 ARTIFICIAL INTELLIGENCE
, 2000
"... We revisit the issue of epistemological and semantic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. We develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the latti ..."
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Cited by 41 (23 self)
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We revisit the issue of epistemological and semantic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. We develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the lattice structure of the collection of all belief pairs. For each logic, we introduce a monotone operator on the lattice of belief pairs. We then show that a whole family of semantics can be defined in a systematic and principled way in terms of fixpoints of this operator (or as fixpoints of certain closely related operators). Our approach elucidates fundamental constructive principles in which agents form their belief sets, and leads to approximation semantics for autoepistemic and default logics. It also allows us to establish a precise onetoone correspondence between the family of semantics for default logic and the family of semantics for autoepistemic logic. The correspondence exploits the modal interpretation of a default proposed by Konolige. Our results establish conclusively that default logic can be viewed as a fragment of autoepistemic logic, a result that has been long anticipated. At the same time, they explain the source of the difficulty to formally relate the semantics of default extensions by Reiter and autoepistemic expansions by Moore. These two semantics occupy different locations in the corresponding families of semantics for default and autoepistemic logics.
Experimenting with Nonmonotonic Reasoning
 IN PROCEEDINGS OF THE 12TH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING
, 1995
"... In this paper, we describe a system, called TheoryBase, whose goal is to facilitate experimental studies of nonmonotonic reasoning systems. TheoryBase generates test default theories and logic programs. It has an identification system for generated theories, which allows us to reconstruct a logic pr ..."
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Cited by 37 (6 self)
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In this paper, we describe a system, called TheoryBase, whose goal is to facilitate experimental studies of nonmonotonic reasoning systems. TheoryBase generates test default theories and logic programs. It has an identification system for generated theories, which allows us to reconstruct a logic program or a default theory from its identifier. Hence, exchanging test cases requires only exchanging identifiers. TheoryBase can generate a large variety of examples of default theories and logic programs. We believe that its universal adoption may significantly advance experimental studies of nonmonotonic reasoning systems.
Extended Logic Programs as Autoepistemic Theories
 In Proceedings of the Second Int'l Workshop on Logic Programming and Nonmonotonic Reasoning
, 1993
"... Recent research on applications of nonmonotonic reasoning to the semantics of logic programs demonstrates that some nonmonotonic formalisms are better suited for such use than others. Circumscription is applicable as long as the programs under consideration are stratified. To describe the semantics ..."
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Cited by 35 (1 self)
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Recent research on applications of nonmonotonic reasoning to the semantics of logic programs demonstrates that some nonmonotonic formalisms are better suited for such use than others. Circumscription is applicable as long as the programs under consideration are stratified. To describe the semantics of general logic programs without the stratification assumption, one has to use autoepistemic logic or default logic. When Gelfond and Lifschitz extended this work to programs with classical negation, they used default logic, because it was not clear whether autoepistemic logic could be applied in that wider domain. In this paper we show that programs with classical negation can be, in fact, easily represented by autoepistemic theories. We also prove that an even simpler embedding is possible if reflexive autoepistemic logic is used. Both translations are applicable to disjunctive programs as well. 1 Introduction Recent research on applications of nonmonotonic reasoning to the semantics of ...
The Inverse Satisfiability Problem
 SIAM Journal on Computing
, 1998
"... We study the complexity of telling whether a set of bitvectors represents the set of all satisfying truth assignments of a Boolean expression of a certain type. We show that the problem is coNPcomplete when the expression is required to be in conjunctive normal form with three literals per clause ..."
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Cited by 31 (6 self)
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We study the complexity of telling whether a set of bitvectors represents the set of all satisfying truth assignments of a Boolean expression of a certain type. We show that the problem is coNPcomplete when the expression is required to be in conjunctive normal form with three literals per clause (3CNF). We also prove a dichotomy theorem analogous to the classical one by Schaefer, stating that, unless P=NP, the problem can be solved in polynomial time if and only if the clauses allowed are all Horn, or all antiHorn, or all 2CNF, or all equivalent to equations modulo two.
Temporal Coherence and Defeasible Knowledge
, 1991
"... We discuss data involving the temporal structure of connected discourse. Questions are raised about the relation between clause order in discourse and causal order in the world, and about the coherence of certain discourses. We maintain that interpretation is contextually influenced by knowledge of ..."
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Cited by 20 (8 self)
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We discuss data involving the temporal structure of connected discourse. Questions are raised about the relation between clause order in discourse and causal order in the world, and about the coherence of certain discourses. We maintain that interpretation is contextually influenced by knowledge of the world and of pragmatics, and that the role of this knowledge should be formalised via a defeasible logic. It transpires that a constrained set of reasoning patterns underlies the retrieval of certain temporal structures. Not all defeasible logics capture the set; the data help choose between candidate logics. We demonstrate that an adequate logic characterises when a text is temporally coherent, reliable and unambiguous relative to the context. We also discuss defeasible reasoning in language generation, and some consequences for the semanticspragmatics interface.
Approximations, Stable Operators, WellFounded Fixpoints And Applications In Nonmonotonic Reasoning
, 2000
"... In this paper we develop an algebraic framework for studying semantics of nonmonotonic logics. Our approach is formulated in the language of lattices, bilattices, operators and fixpoints. The goal is to describe fixpoints of an operator O defined on a lattice. The key intuition is that of an approxi ..."
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Cited by 18 (8 self)
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In this paper we develop an algebraic framework for studying semantics of nonmonotonic logics. Our approach is formulated in the language of lattices, bilattices, operators and fixpoints. The goal is to describe fixpoints of an operator O defined on a lattice. The key intuition is that of an approximation, a pair (x, y) of lattice elements which can be viewed as an approximation to each lattice element z such that x z y. The key notion is that of an approximating operator, a monotone operator on the bilattice of approximations whose fixpoints approximate the fixpoints of the operator O. The main contribution of the paper is an algebraic construction which assigns a certain operator, called the stable operator, to every approximating operator on a bilattice of approximations. This construction leads to an abstract version of the wellfounded semantics. In the paper we show that our theory offers a unified framework for semantic studies of logic programming, default logic and autoepistemic logic.