Implementing Default and Autoepistemic Logics via the Logic of GK

The logic of knowledge and justified assumptions, also known as logic of grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for nonmonotonic reasoning. To date, it has been used to embed in it default logic (propositional case), autoepistemic logic, Turner's logic of universal causation, and general logic programming under stable model semantics. Besides showing the generality of GK as a logic for nonmonotonic reasoning, these embeddings shed light on the relationships among these other logics. In this paper, for the first time, we show how the logic of GK can be embedded into disjunctive logic programming in a polynomial but non-modular translation with new variables. The result can then be used to compute the extension/expansion semantics of default logic, autoepistemic logic and Turner's logic of universal causation by disjunctive ASP solvers such as claspD(-2), DLV, GNT and cmodels.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

G’3-stable semantics and inconsistency

We present an overview on how to perform non-monotonic reasoning based on paraconsistent logics. In particular, we show that one can define a logic programming semantics based on the paraconsistent logic G’3 which is called G’3-stable semantics. This semantics defines a frame for performing non-monotonic reasoning in domains which are pervaded with vagueness and inconsistencies. In fact, we show that, by considering also a possibilistic logic point of view, one can use this extended framework for defining a possibilistic logic programming approach able to deal with reasoning, which is at the same time non-monotonic and uncertain.Peer ReviewedPostprint (published version

Genes and Ant for Defaults Logic

Default Logic and Logic Programming with stable model semantics are recognized as powerful frameworks for incomplete information representation. Their expressive power are suitable for non monotonic reasoning, but the counterpart is their very high level of theoretical complexity. The purpose of this paper is to show how heuristics issued from combinatorial optimization and operation research can be used to built non monotonic reasonning systems

Logic Programming for Describing and Solving Planning Problems

A logic programming paradigm which expresses solutions to problems as stable models has recently been promoted as a declarative approach to solving various combinatorial and search problems, including planning problems. In this paradigm, all program rules are considered as constraints and solutions are stable models of the rule set. This is a rather radical departure from the standard paradigm of logic programming. In this paper we revisit abductive logic programming and argue that it allows a programming style which is as declarative as programming based on stable models. However, within abductive logic programming, one has two kinds of rules. On the one hand predicate definitions (which may depend on the abducibles) which are nothing else than standard logic programs (with their non-monotonic semantics when containing with negation); on the other hand rules which constrain the models for the abducibles. In this sense abductive logic programming is a smooth extension of the standard paradigm of logic programming, not a radical departure.Comment: 8 pages, no figures, Eighth International Workshop on Nonmonotonic Reasoning, special track on Representing Actions and Plannin

The Gödel and the Splitting Translations

When the new research area of logic programming and non-monotonic reasoning emerged at the end of the 1980s, it focused notably on the study of mathematical relations between different non-monotonic formalisms, especially between the semantics of stable models and various non-monotonic modal logics. Given the many and varied embeddings of stable models into systems of modal logic, the modal interpretation of logic programming connectives and rules became the dominant view until well into the new century. Recently, modal interpretations are once again receiving attention in the context of hybrid theories that combine reasoning with non-monotonic rules and ontologies or external knowledge bases. In this talk I explain how familiar embeddings of stable models into modal logics can be seen as special cases of two translations that are very well-known in non-classical logic. They are, first, the translation used by Godel in 1933 to em- ¨ bed Heyting’s intuitionistic logic H into a modal provability logic equivalent to Lewis’s S4; second, the splitting translation, known since the mid-1970s, that allows one to embed extensions of S4 into extensions of the non-reflexive logic, K4. By composing the two translations one can obtain (Goldblatt, 1978) an adequate provability interpretation of H within the Goedel-Loeb logic GL, the system shown by Solovay (1976) to capture precisely the provability predicate of Peano Arithmetic. These two translations and their composition not only apply to monotonic logics extending H and S4, they also apply in several relevant cases to non-monotonic logics built upon such extensions, including equilibrium logic, non-monotonic S4F and autoepistemic logic. The embeddings obtained are not merely faithful and modular, they are based on fully recursive translations applicable to arbitrary logical formulas. Besides providing a uniform picture of some older results in LPNMR, the translations yield a perspective from which some new logics of belief emerge in a natural wa

A logic programming framework for possibilistic argumentation: formalization and logical properties

In the last decade defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning. The logic programming paradigm has shown to be particularly useful for developing different argument-based frameworks on the basis of different variants of logic programming which incorporate defeasible rules. Most of such frameworks, however, are unable to deal with explicit uncertainty, nor with vague knowledge, as defeasibility is directly encoded in the object language. This paper presents Possibilistic Logic Programming (P-DeLP), a new logic programming language which combines features from argumentation theory and logic programming, incorporating as well the treatment of possibilistic uncertainty. Such features are formalized on the basis of PGL, a possibilistic logic based on G¨odel fuzzy logic. One of the applications of P-DeLP is providing an intelligent agent with non-monotonic, argumentative inference capabilities. In this paper we also provide a better understanding of such capabilities by defining two non-monotonic operators which model the expansion of a given program P by adding new weighed facts associated with argument conclusions and warranted literals, respectively. Different logical properties for the proposed operators are studie