Local closed world reasoning:a personal view on current status and trends

1 Introduction In computer science and artificial intelligence,an ontology is a model of (some aspect of) the world that introduces the vocabulary of a particular domain,and specifies the meaning (semantics) of terms.     

Taxonomic reasoning with many-sorted logics

This paper provides an introduction to many-sorted logics and motivates their use for representation and reasoning. Perhaps the most important reason to be interested in many-sorted logic is that computational efficiency can be achieved because the search space can be smaller and the length of a derivation shorter than in unsorted logic. There are many possible many-sorted logics of varying degrees of expressiveness, and the dimensions in which many-sorted logics differ are outlined and logics at various points in this space described. The relationship of many-sorted logic to unsorted logic is discussed and the reason why many-sorted logics derivations may be shorter is demonstrated. The paper concludes with a discussion of some many-sorted logic programming languages and some implementation issues.     

A new fixpoint semantics for general logic programs compared with the well-founded and the stable model semantics

We study a new fixpoint semantics for logic programs with negation. Our construction is intermediate between Van Gelder’s well-founded model and Gelfond and Lifschitz’s stable model semantics. We show first that the stable models of a logic programP are exactly the well-supported models ofP, i.e. the supported models with loop-free finite justifications. Then we associate to any logic programP a non-monotonic operator over the semilattice of justified interpretations, and we define in an abstract form its ordinal powers. We show that the fixpoints of this operator are the stable models ofP, and that its ordinal powers after some ordinala are extensions of the well-founded partial model ofP. In particular ifP has a well-founded model then that canonical model is also an ordinal power and the unique fixpoint of our operator. We show with examples of logic programs which have a unique stable model but no well-founded model that the converse is false. We relate also our work to Doyle’s truth maintenance system and some implementations of rule-based expert systems.     

On the formal semantics of IF-like logics

In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Independence Friendly (IF) logics. In this paper we argue that this is not an inherent characteristic of these logics but a defect in the way in which the compositional semantics given by Hodges for the regular fragment was generalized to arbitrary formulas. We fix this by proposing an alternative formalization, based on a variation of the classical notion of valuation. Basic metatheoretical results are proven. We present these results for Hodges' slash logic (from which these can be easily transferred to other IF-like logics) and we also consider the flattening operator, for which we give novel game-theoretical semantics.     

Substantial and formal deductions in logics with vector semantics

The problem of logic deduction for one class of logics with a vector semantics is discussed. In the given logics the trustiness is represented by a vector with components 〈Truth; Lie〉, which do not depend on each other. The problem of organization of “substantial” and “formal” deductions is considered. In the first case the meaning of truth (semantics) of judgements is taken into account, whereas in the second case only the structure of judgements (syntax) is considered.     

An Algorithm for Determining Database Consistency Under the Closed World Assumption

It is well-known that there are circumstances where applying Reiter‘s closed world assumption(CWA)will lead to logical inconsistencies.In this paper,a new characterization of the CA consistency is pesented and an algorithm is proposed for determining whether a datalase without function symbols is consistent with the CWA.The algorithm is shown to be efficient.     

Autoepistemic logics as a unifying framework for the semantics of logic programs

In this paper, it is shown that a three-valued autoepistemic logic provides an elegant unifying framework for some of the major semantics of normal and disjunctive logic programs and logic programs with classical negation, namely, the stable semantics, the well-founded semantics, supported models, Fitting's semantics, Kunen's semantics, the stationary semantics, and answer sets. For the first time, so many semantics are embedded into one logic. The framework extends previous results—by Gelfond, Lifschitz, Marek, Subrahmanian, and Truszczynski —on the relationships between logic programming and Moore's autoepistemic logic. The framework suggests several new semantics for negation-as-failure. In particular, we will introduce the epistemic semantics for disjunctive logic programs. In order to motivate the epistemic semantics, an interesting class of applications called ignorance tests will be formalized; it will be proved that ignorance tests can be defined by means of the epistemic semantics, but not by means of the old semantics for disjunctive programs. The autoepistemic framework provides a formal foundation for an environment that integrates different forms of negation. The role of classical negation and various forms of negation-by-failure in logic programming will be briefly discussed.