Revised Stable Models-a new semantics for logic programs (original) (raw)
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Revised Stable Models - A Semantics for Logic Programs
2005
This paper introduces an original 2-valued semantics for Normal Logic Programs (NLP), which conservatively extends the Stable Model semantics (SM) to all normal programs. The distinction consists in the revision of one feature of SM, namely its treatment of odd loops, and of infinitely long support chains, over default negation. This single revised aspect, addressed by means of a Reductio ad Absurdum approach, affords a number of fruitful consequences, namely regarding existence, relevance and top-down querying, cumulativity, and implementation. The paper motivates and defines the Revised Stable Models semantics (rSM), justifying and exemplifying it. Properties of rSM are given and contrasted with those of SM. Furthermore, these results apply to SM whenever odd loops and infinitely long chains over negation are absent, thereby establishing significant, not previously known, properties of SM. Conclusions, further work, terminate the paper.
2011
After a very brief introduction to the general subject of Knowledge Representation and Reasoning with Logic Programs we analyse the syntactic structure of a logic program and how it can influence the semantics. We outline the important properties of a 2-valued semantics for Normal Logic Programs, proceed to define the new Minimal Hypotheses semantics with those properties and explore how it can be used to benefit some knowledge representation and reasoning mechanisms. The main original contributions of this work, whose connections will be detailed in the sequel, are: • The Layering for generic graphs which we then apply to NLPs yielding the Rule Layering and Atom Layering-a generalization of the stratification notion; • The Full shifting transformation of Disjunctive Logic Programs into (highly nonstratified) NLPs; • The Layer Support-a generalization of the classical notion of support; • The Brave Relevance and Brave Cautious Monotony properties of a 2-valued semantics; • The notions of Relevant Partial Knowledge Answer to a Query and Locally Consistent Relevant Partial Knowledge Answer to a Query; • The Layer-Decomposable Semantics family-the family of semantics that reflect the above mentioned Layerings; • The Approved Models argumentation approach to semantics; • The Minimal Hypotheses 2-valued semantics for NLP-a member of the Layer-Decomposable Semantics family rooted on a minimization of positive hypotheses assumption approach; • The definition and implementation of the Answer Completion mechanism in XSB Prolog-an essential component to ensure XSB's WAM full compliance with the Well-Founded Semantics; • The definition of the Inspection Points mechanism for Abductive Logic Programs; ix x • An implementation of the Inspection Points workings within the Abdual system [21] We recommend reading the chapters in this thesis in the sequence they appear. However, if the reader is not interested in all the subjects, or is more keen on some topics rather than others, we provide alternative reading paths as shown below. 1-2-3-4-5-6-7-8-9-12 Definition of the Layer-Decomposable Semantics family and the Minimal Hypotheses semantics (1 and 2 are optional) 3-6-7-8-10-11-12 All main contributions-assumes the reader is familiarized with logic programming topics 3-4-5-10-11-12 Focus on abductive reasoning and applications
Extending negation as failure by abduction: A three-valued stable model semantics
The Journal of Logic Programming, 1996
In this paper, we propose a semantics for logic programs with negation as failure, the Finite Failure Stable Model semantics (FF-SM semantics), which is a three-valued extension of Gelfond and Lifschitz' Stable Model semantics. FF-SM semantics is defined in the style of Gelfond and Lifschitz Stable Model semantics, but it builds on an underlying Kripke/Kleene semantics, in which loops causing nonterminating computations are modeled by means of the truth-value undefined. It is different from the eXtended Stable Model (XSM) semantics defined by Przymusinski, since it does not capture infinite failure. We also introduce an abductive proof procedure which is an abductive extension of SLDNF-resolution based on the ideas underlying Eshghi and Kowalski's abductive procedure. We prove that our procedure is sound and complete with respect to FF-SM semantics. We compare the FF-SM semantics with the XSM semantics, and provide a reconstruction for it within the bilatticebased framework proposed by Fitting. In the paper, we deal with the propositional case.
Strong negation in well-founded and partial stable semantics for logic programs
2006
Abstract. A formalism called partial equilibrium logic (PEL) has recently been proposed as a logical foundation for the well-founded semantics (WFS) of logic programs. In PEL one defines a class of minimal models, called partial equilibrium models, in a non-classical logic, HT2. On logic programs partial equilibrium models coincide with Przymusinski's partial stable (p-stable) models, so that PEL can be seen as a way to extend WFS and p-stable semantics to arbitrary propositional theories.
Theoretical Computer Science, 1992
Marek, W., and V.S. Subrahmanian, The relationship between stable, supported, default and autoepistemic semantics for general logic programs, Theoretical Computer Science 103 (1992) 365-386. We investigate the relationship between various alternative semantics for logic programming, viz. the stable model semantics of Gelfond and Lifschitz (1988), the supported model semantics as developed by Apt, Blair and Walker (1988), autoepistemic translations (cf. Moore (1985)) of general logic programs and default translations of general logic programs, Reiter (1980).
Back and forth semantics for normal, disjunctive and extended logic programs
1998
Abstract We de ne a logical semantics called back-and-forth, applicable to normal and disjunctive datalog programs as well as to programs possessing a second, explicit orstrong'negation operator. We show that on normal programs it is equivalent to the well-founded semantics (WFS), and that on disjunctive programs it is equivalent to the P-stable semantics of Eiter, Leone and Sacc a, hence to Przymusinski's 3-valued stable semantics.
Stable models and non-determinism in logic programs with negation
Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '90, 1990
Previous researchers have proposed generalizations of Horn clause logic to support negation and nondeterminism as two separate extensions. In this paper, we show that the stable model semantics for logic programs provides a unitied basis for the treatment of both concepts. Fit, we introduce the concepts of partial models, stable models, strongly founded models and deterministic models and other interesting classes of partial models and study their relationships. We show that the maximal determini stic model of a program is a subset of the intersection of all its stable models and that the well-founded model of a program is a subset of its maximal det erministic model. Then, we show that the use of stable models subsumes the use of the non-deterministic choice construct in LDL and provides an alternative definition of the semantics of this construct. Finally, we provide a constructive definition for stable models with the introduction of a procedure, called buc~ruckingfkpoint, that nondeterministically constructs a total stable model, if such a model exists.
Stable versus layered logic program semantics
2009
Abstract. For practical applications, the use of top-down query-driven proofprocedures is convenient for an efficient use and computation of answers using Logic Programs as knowledge bases. Additionally, abductive reasoning on demand is intrinsically a top-down search method. A 2-valued semantics for Normal Logic Programs (NLPs) allowing for top-down query-solving is thus highly desirable, but the Stable Models semantics (SM) does not allow it, for lack of the relevance property.
Approved models for normal logic programs
2007
We introduce an original 2-valued semantics for Normal Logic Programs (NLPs) extending the well-known Argumentation work of Phan Minh Dung on Admissible Arguments and Preferred Extensions. In the 2-valued Approved Models Semantics set forth, an Approved Model (AM) correspond to the minimal positive strict consistent 2-valued completion of a Dung Preferred Extension.
Smodels — an implementation of the stable model and well-founded semantics for normal logic programs
Lecture Notes in Computer Science, 1997
The Smodels system is a C++ implementation of the wellfounded and stable model semantics for range-restricted function-free normal programs. The system includes two modules: (i) smodels which implements the two semantics for ground programs and (ii) parse which computes a grounded version of a range-restricted function-free normal program. The latter module does not produce the whole set of ground instances of the program but a subset that is su cient in the sense that no stable models are lost. The implementation of the stable model semantics for ground programs is based on bottom-up backtracking search where a powerful pruning method is employed. The pruning method exploits an approximation technique for stable models which is closely related to the well-founded semantics. One of the advantages of this novel technique is that it can be implemented to work in linear space. This makes it possible to apply the stable model semantics also in areas where resulting programs are highly non-strati ed and can possess a large number of stable models. The implementation has been tested extensively and compared with a state of the art implementation of the stable model semantics, the SLG system. In tests involving ground programs it clearly outperforms SLG.