In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs We demonstrate that inherent features of stable model semantics naturally lead to a logic programming system that offers an interesting alternative to more traditional logic programming styles of Horn logic programming, stratified logic programming and logic programming with well-founded semantics The proposed approach is based on the interpretation of program clauses as constraints In this setting, a program does not describe a single intended model, but a family of its stable models These stable models encode solutions to the constraint satisfaction problem described by the program Our approach imposes restrictions on the syntax of logic programs In particular, function symbols are eliminated from the language We argue that the resulting logic programming system is well-attuned to problems in the class NP, has a well-defined domain of applications, and an emerging methodology of programming We point out that what makes the whole approach viable is recent progress in implementations of algorithms to compute stable models of propositional logic programs

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Stable Models and an Alternative Logic Programming Paradigm

Combining answer set programming with description logics for the Semantic Web

We address the problem of authorization in large-scale, open, distributed systems. Authorization decisions are needed in electronic commerce, mobile-code execution, remote resource sharing, privacy protection, and many other applications. We adopt the trust-management approach, in which "authorization" is viewed as a "proof-of-compliance" problem: Does a set of credentials prove that a request complies with a policy?We develop a logic-based language, called Delegation Logic (DL), to represent policies, credentials, and requests in distributed authorization. In this paper, we describe D1LP, the monotonic version of DL. D1LP extends the logic-programming (LP) language Datalog with expressive delegation constructs that feature delegation depth and a wide variety of complex principals (including, but not limited to, k-out-of-n thresholds). Our approach to defining and implementing D1LP is based on tractably compiling D1LP programs into ordinary logic programs (OLPs). This compilation approach enables D1LP to be implemented modularly on top of existing technologies for OLP, for example, Prolog.As a trust-management language, D1LP provides a concept of proof-of-compliance that is founded on well-understood principles of logic programming and knowledge representation. D1LP also provides a logical framework for studying delegation.

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Delegation logic: A logic-based approach to distributed authorization

This paper is a survey and critical overview of recent work on the extension of Logic Programming to perform Abductive Reasoning (Abductive Logic Programming). It updates the earlier paper \Abductive Logic Programming" 88]. We outline the general framework of Abduction and its applications to Knowledge Assimilation and Default Reasoning; we describe the argumentation-theoretic approach to the use of abduction as an interpretation for Negation as Failure, introduced in the earlier version 88] of this paper; and we present recent work on the generalisation of the argumentation-theoretic approach to provide a framework for default reasoning in general. We also analyse the links between Abduction and Constraint Logic Programming, as well as between Abduction and the extension of Logic Programming obtained by adding a form of explicit negation. Finally we discuss the relation between Abduction and Truth Maintenance.

The role of abduction in logic programming

In this paper, we examine an argument-based semantics called semi-stable semantics. Semi-stable semantics is quite close to traditional stable semantics in the sense that every stable extension is also a semi-stable extension. One of the advantages of semi-stable semantics is that there exists at least one semi-stable extension. Furthermore, if there also exists at least one stable extension, then the semi-stable extensions coincide with the stable extensions. This, and other properties, make semi-stable semantics an attractive alternative for the more traditional stable semantics, which until now has been widely used in fields such as logic programming and answer set programming.

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Semi-Stable Semantics

In this paper we define the rather general framework of Monotonic Logic Programs, where the main results of (definite) logic programming are validly extrapolated. Whenever defining new logic programming extensions, we can thus turn our attention to the stipulation and study of its intuitive algebraic properties within the very general setting. Then, the existence of a minimum model and of a monotonic immediate consequences operator is guaranteed, and they are related as in classical logic programming. Afterwards we study the more restricted class of residuated logic programs which is able to capture several quite distinct logic programming semantics. Namely: Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic Logic Programming. We provide the embedding of possibilistic logic programming.

Monotonic and Residuated Logic Programs

Our contribution to this volume consists in giving a logic programmer’s view on handling program inconsistency. The semantics we cover will touch several aspects of implementing reasoning in the presence of contradiction. Logic programming has already shown a wide applicability for representings knowledge [Barai and Gel-fond, 1994]. Also, the most important non-monotonic formalisms, for instance Default Logic [Reiter, 1980] and Autoepistemic logics [Moore, 1984; Moore, 1985], have a counterpart semantics on the logic programming side.1 Moreover, logic programming has turned out to be vehicle for implementing and exploring other important aspects of Artificial Intelligence such as updates and belief revision. Therefore, it is not strange that a lot of work in the logic programming community has been carried out to understand the integration of paraconsistent reasoning with logic programming, in preparation for an applicational and implementational role of great potential, now emerging.

A survey of paraconsistent semantics for logic programs

The evolution of logic programming semantics has included the introduction of a new explicit form of negation, beside the older implicit (or default) negation typical of logic programming. The richer language has been shown adequate for a spate of knowledge representation and reasoning forms.

A logic programming system for nonmonotonic reasoning

This chapter contains sections titled: Introduction, Language, Revising Contradictory Extended Logic Programs, Application to Declarative Debugging, Application to Diagnosis, Acknowledgements, References

Diagnosis and debugging as contradiction removal

A general framework of logic programming allowing for the combination of several adjoint lattices of truth-values is presented. The main contribution is a new sufficient condition which guarantees termination of all queries for the fixpoint semantics for an interesting class of programs. Several extensions of these conditions are presented and related to some well-known formalisms for probabilistic logic programming.

Carlos Viegas Damásio

Papers

Monotonic and Residuated Logic Programs

A survey of paraconsistent semantics for logic programs

A logic programming system for nonmonotonic reasoning

Diagnosis and debugging as contradiction removal

Sorted Multi-adjoint Logic Programs: Termination Results and Applications