Annotated logics were introduced in [43] and later studied in [5, 7, 31, 32]. In [32], annotations were extended to allow variables and functions, and it was argued that such logics can be used to provide a formal semantics for rule-based expert systems with uncertainty. In this paper, we continue to investigate the power of this approach. First, we introduce a new semantics for such programs based on ideals of lattices. Subsequently, some proposals for multivalued logic programming [5, 7, 18, 32, 40, 47] as well as some formalisms for temporal reasoning [1, 3, 41] are shown to fit into this framework. As an interesting byproduct of the investigation, we obtain a new result concerning multivalued logic programming: a model theory for Fitting's bilattice-based logic programming, which until now has not been characterized model-theoretically. This is accompanied by a corresponding proof theory.

Theory of generalized annotated logic programming and its applications

Fuzzy sets in approximate reasoning, part 2: logical approaches

An approach to automated deduction under uncertainty, based on possibilistic logic, is described; for that purpose we deal with clauses weighted by a degree that is a lower bound of a necessity or a possibility measure, according to the nature of the uncertainty. Two resolution rules are used for coping with the different situations, and the classical refutation method can be generalized with these rules. Also, the lower bounds are allowed to be functions of variables involved in the clauses, which results in hypothetical reasoning capabilities. In cases where only lower bounds of necessity measures are involved, a semantics is proposed in which the completeness of the extended resolution principle is proved. The relation between our approach and the idea of minimizing abnormality is briefly discussed. Moreover, deduction from a partially inconsistent knowledge base can be managed in this approach and captures a form of nonmonotonicity. >

Automated reasoning using possibilistic logic: semantics, belief revision, and variable certainty weights

Approximate reasoning by similarity-based SLD resolution

A careful distinction is made between fuzzy propositions (i.e., propositions involving vague predicates) that may have intermediary degrees of truth, and uncertain propositions (with nonvague predicates) the truth or falsity of which cannot definitely be established due to the incompleteness of the available information. Then the resolution principle is extended in the case of uncertain propositions where the uncertainty is modeled in terms of necessity measures. The alternative use of probability measures or of Shafer's belief functions is also discussed.

Necessity Measures and the Resolution Principle

Prolog-ELF incorporating fuzzy logic and several useful functions into Prolog has been implemented as a basic language for building knowledge systems with uncertainty or fuzziness. Prolog-ELF inherits all the desirable basic features of Prolog. In addition to assertions with truth-values between 1.0 and 0.5 (0 for exceptional cases), fuzzy sets can be very easily manipulated. An application of fuzzy logical database is illustrated.

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Naoki Kanai

Papers

Prolog-ELF incorporating fuzzy logic