132 research outputs found
Epistemic Foundation of Stable Model Semantics
Stable model semantics has become a very popular approach for the management
of negation in logic programming. This approach relies mainly on the closed
world assumption to complete the available knowledge and its formulation has
its basis in the so-called Gelfond-Lifschitz transformation.
The primary goal of this work is to present an alternative and
epistemic-based characterization of stable model semantics, to the
Gelfond-Lifschitz transformation. In particular, we show that stable model
semantics can be defined entirely as an extension of the Kripke-Kleene
semantics. Indeed, we show that the closed world assumption can be seen as an
additional source of `falsehood' to be added cumulatively to the Kripke-Kleene
semantics. Our approach is purely algebraic and can abstract from the
particular formalism of choice as it is based on monotone operators (under the
knowledge order) over bilattices only.Comment: 41 pages. To appear in Theory and Practice of Logic Programming
(TPLP
Shinren : Non-monotonic trust management for distributed systems
The open and dynamic nature of modern distributed systems and pervasive environments presents significant challenges to security management. One solution may be trust management which utilises the notion of trust in order to specify and interpret security policies and make decisions on security-related actions. Most trust management systems assume monotonicity where additional information can only result in the increasing of trust. The monotonic assumption oversimplifies the real world by not considering negative information, thus it cannot handle many real world scenarios. In this paper we present Shinren, a novel non-monotonic trust management system based on bilattice theory and the anyworld assumption. Shinren takes into account negative information and supports reasoning with incomplete information, uncertainty and inconsistency. Information from multiple sources such as credentials, recommendations, reputation and local knowledge can be used and combined in order to establish trust. Shinren also supports prioritisation which is important in decision making and resolving modality conflicts that are caused by non-monotonicity
An encompassing framework for Paraconsistent Logic Programs
AbstractWe propose a framework which extends Antitonic Logic Programs [Damásio and Pereira, in: Proc. 6th Int. Conf. on Logic Programming and Nonmonotonic Reasoning, Springer, 2001, p. 748] to an arbitrary complete bilattice of truth-values, where belief and doubt are explicitly represented. Inspired by Ginsberg and Fitting's bilattice approaches, this framework allows a precise definition of important operators found in logic programming, such as explicit and default negation. In particular, it leads to a natural semantical integration of explicit and default negation through the Coherence Principle [Pereira and Alferes, in: European Conference on Artificial Intelligence, 1992, p. 102], according to which explicit negation entails default negation. We then define Coherent Answer Sets, and the Paraconsistent Well-founded Model semantics, generalizing many paraconsistent semantics for logic programs. In particular, Paraconsistent Well-Founded Semantics with eXplicit negation (WFSXp) [Alferes et al., J. Automated Reas. 14 (1) (1995) 93–147; Damásio, PhD thesis, 1996]. The framework is an extension of Antitonic Logic Programs for most cases, and is general enough to capture Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs, and Fuzzy Logic Programming. Thus, we have a powerful mathematical formalism for dealing simultaneously with default, paraconsistency, and uncertainty reasoning. Results are provided about how our semantical framework deals with inconsistent information and with its propagation by the rules of the program
An analysis of the equational properties of the well-founded fixed point
Well-founded fixed points have been used in several areas of knowledge
representation and reasoning and to give semantics to logic programs involving
negation. They are an important ingredient of approximation fixed point theory.
We study the logical properties of the (parametric) well-founded fixed point
operation. We show that the operation satisfies several, but not all of the
equational properties of fixed point operations described by the axioms of
iteration theories
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