Weak and Strong Disjunction in Possibilistic ASP

2010

Querying over disjunctive ASP with functions is a highly undecidable task in general. In this paper we focus on disjunctive logic programs with stratified negation and functions under the stable model semantics (ASP fs ). We show that query answering in this setting is decidable, if the query is finitely recursive (ASP fs fr ). Our proof yields also an effective method for query evaluation. It is done by extending the magic set technique to ASP fs fr . We show that the magic-set rewritten program is query equivalent to the original one (under both brave and cautious reasoning). Moreover, we prove that the rewritten program is also finitely ground, implying that it is decidable. Importantly, finitely ground programs are evaluable using existing ASP solvers, making the class of ASP fs fr queries usable in practice.

international conference on logic programming, 2012

We introduce the class of possibilistic nested logic programs. These possibilistic logic programs allow us to use nested expressions in the bodies and the heads of their rules. By considering a possibilistic nested logic program as a possibilistic theory, a construction of a possibilistic logic programing semantics based on answer sets for nested logic programs and the proof theory of possibilistic logic is defined. We show that this new semantics for possibilistic logic programs is computable by means of transforming possibilistic nested logic programs into possibilistic disjunctive logic programs. The expressiveness of the possibilistic nested logic programs is illustrated by scenarios from the medical domain. In particular, we exemplify how possibilistic nested logic programs are expressive enough for capturing medical guidelines which are pervaded of vagueness and qualitative information.

2008

§ , since it better constrains the set of possible worlds. Since a formula is interpreted in the least informative information state which satisfies it, we have two possible readings for negation: the first is the modal one, which refers to information which is absent in a given information state. In this case the statement ! ¡ ¢ ¦ must be read as: "in the given state of information it is not possible to prove that ¦ is necessary at least ¡ (while it may become possible in a refinement of the information state)". The second interpretation for negation, which we use in our logic, is an internal one, in the sense that the statement

Journal of Automated Reasoning, 1993

This paper studies a strong form of disjunctive information in deductive databases. The basic idea is that a disjunction A v B should be considered true only in the case when neither A nor B can be inferred, but the disjunction A v B is true. Under this interpretation, databases may be inconsistent. For those databases that are consistent, it is shown that a unique minimal model exists. We study a fixpoint theory and present a sound and complete proof procedure for query processing in consistent databases. For a class of inconsistent databases, we obtain a declarative semantics by selecting an interpretation that maximizes satisfaction, and minimizes indefiniteness. Two notions of negation are introduced.

Lecture Notes in Computer Science, 1998

In this paper, we use autoepistemic reasoning semantics to classify various semantics for disjunctive logic programs with default negation. We have observed that two different types of negative introspection in autoepistemic reasoning present two different interpretations of default negation: consistency-based and minimal-model-based. We also observed that all logic program semantics fall into three semantical points of view: the skeptical, stable, and partial-stable. Based on these two observations, we classify disjunctive logic program semantics into six different categories, and discuss the relationships among various semantics. We say α cannot be derived from Π under any circumstance if α cannot be derived from Π N for any set N of default negations. Note that Π N is a program obtained

… Engineering for Answer …, 2009

Over the last ten years, answer set programming (ASP) has grown from a pure theoretical knowledge representation and reasoning formalism to a computational approach with a very strong formal backing. At present, ASP is seen as the computational embodiment of non-monotonic reasoning incorporating techniques of databases, knowledge representation, logic and constraint programming. ASP has become an appealing tool for knowledge representation and reasoning and thanks to the increasing efficiency of the implementations of ASP solvers, the field has now started to tackle many industrially-relevant applications.

2016

Probabilistic logic programs without negation can have cycles (with a preference for false), but cannot represent all conditional distributions. Probabilistic logic programs with negation can represent arbitrary conditional probabilities, but with cycles they create logical inconsistencies. We show how allowing negative noise probabilities allows us to represent arbitrary conditional probabilities without negations. Noise probabilities for non-exclusive rules are difficult to interpret and unintuitive to manipulate; to alleviate this we define "probability-strengths" which provide an intuitive additive algebra for combining rules. For acyclic programs we prove what constraints on the strengths allow for proper distributions on the non-noise variables and allow for all non-extreme distributions to be represented. We show how arbitrary CPDs can be converted into this form in a canonical way. Furthermore, if a joint distribution can be compactly represented by a cyclic progra...

Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) accor?i � g to their level of certainty, while the latter exhibits relationships between variables. The two types of representations are semantically equivalent when they lead to the same possibility distribution (which rank orders the possible interpretations). A possibility distribution can be decomposed using a chain rule which may be based on two different kinds of conditioning which exist in possibility theory (one based on product in a numerical setting, one based on minimum operation in a qualitative setting). These two types of conditioning induce two ki n_ ds of possibilistic graphs. In both cases, a translatiOn of these graphs into possibilistic bases is provided. The converse translation from a possibilistic knowledge base into a min-based graph is also described.

Proceedings of the artificial intelligence 6th …, 2007

Uncertain information is present in many real applications e.g., medical domain, weather forecast, etc. The most common approaches for leading with this information are based on probability however some times; it is difficult to find suitable probabilities about some events. In this paper, we present a possibilistic logic programming approach which is based on possibilistic logic and PStable semantics. Possibilistic logic is a logic of uncertainty tailored for reasoning under incomplete evidence and Pstable Semantics is a solid semantics which emerges from the fusion of non-monotonic reasoning and logic programming; moreover it is able to express answer set semantics, and has strong connections with paraconsistent logics.