Results 1  10
of
14
Classical Negation in Logic Programs and Disjunctive Databases
 New Generation Computing
, 1991
"... An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic progra ..."
Abstract

Cited by 852 (74 self)
 Add to MetaCart
An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negationasfailure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter. 1 Introduction An important limitation of traditional logic programming as a knowledge representation tool, in comp...
Logic Programming and Negation: A Survey
 JOURNAL OF LOGIC PROGRAMMING
, 1994
"... We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them. ..."
Abstract

Cited by 242 (8 self)
 Add to MetaCart
We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them.
Logic Programming and Knowledge Representation
 Journal of Logic Programming
, 1994
"... In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and sh ..."
Abstract

Cited by 224 (21 self)
 Add to MetaCart
In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and show how each of the added features extends the representational power of the language.
Dualities between Alternative Semantics for Logic Programming and Nonmonotonic Reasoning
 Journal of Automated Reasoning
, 1998
"... The GelfondLifschitz operator [GL88] associated with a logic program (and likewise the operator associated with default theories by Reiter) exhibits oscillating behavior. In the case of logic programs, there is always at least one finite, nonempty collection of Herbrand interpretations around whic ..."
Abstract

Cited by 88 (8 self)
 Add to MetaCart
The GelfondLifschitz operator [GL88] associated with a logic program (and likewise the operator associated with default theories by Reiter) exhibits oscillating behavior. In the case of logic programs, there is always at least one finite, nonempty collection of Herbrand interpretations around which the GelfondLifschitz [GL88] operator "bounces around". The same phenomenon occurs with default logic when Reiter's operator \Gamma \Delta is considered. Based on this, a "stable class" semantics and "extension class" semantics was proposed in [BS90]. The main advantage of this semantics was that it was defined for all logic programs (and default theories), and that this definition was modelled using the standard operators existing in the literature such as Reiter's \Gamma \Delta operator. In this paper, our primary aim is to prove that there is a very interesting duality between stable class theory and the well founded semantics for logic programming. In the stable class semantics, class...
Nonmonotonic Reasoning with Well Founded Semantics
 Proc. of 8th ICLP
, 1991
"... Well Founded Semantics is adequate to capture nonmonotonic reasoning if we interpret the Well Founded model of a program P as a (possibly incomplete) view of the world. Thus the Well Founded model may be accepted to be a definite view of the world and the extended stable models as alternative enlarg ..."
Abstract

Cited by 43 (26 self)
 Add to MetaCart
Well Founded Semantics is adequate to capture nonmonotonic reasoning if we interpret the Well Founded model of a program P as a (possibly incomplete) view of the world. Thus the Well Founded model may be accepted to be a definite view of the world and the extended stable models as alternative enlarged consistent belief models an agent may have about the world. Our purpose is to exhibit a modular systematic method of representing nonmonotonic problems with the Well Founded semantics of logic programs. In this paper we use this method to represent and solve some classical nonmonotonic problems. This leads us to consider our method quite generic. 1 Introduction Well Founded Semantics (WFS) [15] is adequate to capture nonmonotonic reasoning if we interpret the Well Founded model (WFM) of a program P as a (possibly incomplete) view of the world. Thus the WFM may be accepted to be a definite view of the world and the eXtended Stable Models (XSMs) as alternative enlarged consistent belief mo...
Counterfactual Reasoning Based on Revising Assumptions
, 1991
"... We present a semantics for counterfactual implication relative to positive programs with integrity constraints and protected rules (unrevisable). A counterfactual truth evaluation is presented based on Contradiction Removal Semantics. We show the adequacy of CRS to define the notion of similarity ne ..."
Abstract

Cited by 23 (13 self)
 Add to MetaCart
We present a semantics for counterfactual implication relative to positive programs with integrity constraints and protected rules (unrevisable). A counterfactual truth evaluation is presented based on Contradiction Removal Semantics. We show the adequacy of CRS to define the notion of similarity needed for defining counterfactual truth. The concepts introduced by CRS are adequate to support the revision process required by contravening hypoteses when evaluating counterfactuals. 1 Introduction We present a semantics for counterfactual implication relative to positive logic programs with integrity constraints and protected (unrevisable) rules.The Contradiction Removal Semantics (CRS ) [PAA91a] setting employed is a suitable extension to well founded model semantics (WFS) [VGRS90], to deal with classical negation and contradiction, by allowing the revising of assumptions. Lewis [Lew73] is a classic essay on counterfactuals, and our basic definitions and concepts drawn on it. In the next...
On the Complexity of Entailment in Propositional Multivalued Logics
, 1997
"... Multivalued logics have a long tradition in the philosophy and logic literature that originates from the work by / Lukaszewicz in the 20's. More recently, many AI researchers have been interested in this topic for both semantic and computational reasons. Multivalued logics have indeed been frequentl ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
Multivalued logics have a long tradition in the philosophy and logic literature that originates from the work by / Lukaszewicz in the 20's. More recently, many AI researchers have been interested in this topic for both semantic and computational reasons. Multivalued logics have indeed been frequently used both for their semantic properties and as tools for designing tractable reasoning systems. We focus here on the computational aspects of multivalued logics. The main result of this paper is a detailed picture of the impact that the semantic definition, the syntactic form and the assumptions on the relative sizes of the inputs have on the complexity of entailment checking. In particular we show new polynomial cases and generalize polynomial cases already known in the literature for various popular multivalued logics. Such polynomial cases are obtained by means of two simple algorithms, sharing a common method. Dipartimento di Informatica e Sistemistica, Universit`a di Roma "La Sapien...
Autoepistemic Logic As A Unified Basis For Nonmonotonic Reasoning
, 1993
"... Autoepistemic logic is investigated in a general setting where autoepistemic reasoning based on a given classical logic is studied. The possible sets of autoepistemic conclusions from a set of premises are defined in terms of expansions of the premises. First Moore style expansions defined by a fixe ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Autoepistemic logic is investigated in a general setting where autoepistemic reasoning based on a given classical logic is studied. The possible sets of autoepistemic conclusions from a set of premises are defined in terms of expansions of the premises. First Moore style expansions defined by a fixed point equation are considered and a simple finitary characterization of expansions is developed. An alternative definition is proposed where autoepistemic reasoning is formalized as a sequence of introspection steps using an enumeration of sentences. The resulting enumerationbased expansions are a proper subclass of Moore style expansions. An even more tightly grounded subclass is captured by considering only Lhierarchic enumerations. Finitary characterizations of enumerationbased and Lhierarchic expansions are developed. It is shown that autoepistemic reasoning based on Moore style, enumerationbased, and Lhierarchic expansions is decidable if the monotonic consequence relation giv...
Weakened Negative Introspection in Autoepistemic Reasoning
 IN PROCEEDINGS OF THE 3RD KURT G#DEL COLLOQUIUM ON COMPUTATIONAL LOGIC AND PROOF THEORY
, 1993
"... A new weakened scheme for negative introspection in autoepistemic reasoning is proposed. The scheme is formulated prooftheoretically in terms of enumerations of formulae. The resulting sets of conclusions based on this negative introspection principle, cautious autoepistemic expansions, generalize ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
A new weakened scheme for negative introspection in autoepistemic reasoning is proposed. The scheme is formulated prooftheoretically in terms of enumerations of formulae. The resulting sets of conclusions based on this negative introspection principle, cautious autoepistemic expansions, generalize Moore style stable expansions such that every set of premises has a cautious expansion. A finitary characterization is developed for cautious expansions. The elimination of weakly grounded cautious expansions yields a subclass of cautious expansions: the Ngrounded cautious expansions. The least Ngrounded cautious expansion is shown to be unique and the intersection of all Ngrounded cautious expansions. This is in contrast with Moore style stable expansions. The least Ngrounded cautious expansion can be constructed iteratively as the least fixed point of a monotonic operator. Such a construction is exceptional, since autoepistemic expansions are nonconstructive in general. It is also s...
Inheritance Reasoning: Psychological Plausibility, Proof Theory and Semantics
, 1995
"... Default inheritance reasoning is a propositional approach to nonmonotonic reasoning designed to model reasoning with natural language generics. Inheritance reasoners model sets of natural language generics as directed acyclic graphs, and inference corresponds to the specification of paths through th ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Default inheritance reasoning is a propositional approach to nonmonotonic reasoning designed to model reasoning with natural language generics. Inheritance reasoners model sets of natural language generics as directed acyclic graphs, and inference corresponds to the specification of paths through those networks. A proliferation of inheritance proof theories exist in the literature along with extensive debate about the most reasonable way to construct inferences, based on intuitions about interpretations of particular inheritance networks. There has not been an accepted semantics for inheritance which unifies the set of possible proof theories, which would help identify truly illmotivated proof theories. This thesis attempts to clarify the inheritance literature in the three ways indicated in the title: psychological plausibility, proof theory and semantics. The thesis intends to displace debate about the best inferences to draw about a network from logicians ' introspections to empiri...