Toshiharu Waragai

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One of the well-known systems of para consistent logic called {\bf LFI1} is designed to be a base system in constructing evolutionary databases. This system {\bf LFI1} is proved to be a 3-valued logic and also maximal relative to classical logic enriched with inconsistency operator in an obvious manner. The present paper aims to examine the system {\bf(More)
Defeasible logic is an efficient logic for defeasible reasoning. It is defined through a proof theory and, until now, has had no model theory. In this paper a model-theoretic semantics is given for defeasible logic. The logic is sound and complete with respect to the semantics. We also briefly outline how this approach extends to a wide range of defeasible(More)
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge-based systems, logical semantics(More)
Properties of classical (logical) entailment relation (denoted as ⊢) have been well studied and well-understood, either with or without the presence of logical connectives. There is, however, less uniform agreement on laws for the nonmonotonic consequence relation. This paper studies axioms for nonmonotonic consequences from a semantics-based point of view,(More)
The model theory of a first-order logic called N is introduced. N does not eliminate double negations, as classical logic does, but instead reduces fourfold negations. N is very close to classical logic: N has two truth values; implications are, in N like in classical logic, material; and negation distributes over compound formulas in N as it does in(More)
Signed systems were introduced as a general, syntaxindependent framework for paraconsistent reasoning, that is, nontrivialised reasoning from inconsistent information. In this paper, we show how the family of corresponding paraconsistent consequence relations can be axiomatised by means of quantified Boolean formulas. This approach has several benefits.(More)
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge-based systems, logical semantics(More)