Seiki Akama

Many-valued and annotated modal logics

Many-valued modal logics are of interest from theoretical and practical point of view. Unfortunately, there are no unified theoretical frameworks for many-valued modal logics. We sketch their foundations based on the so-called annotated logics. We give a Kripke semantics for annotated modal logics and prove the completeness theorem. We also discuss possible applications of annotated modal logics to AI.

Subformula semantics for strong negation systems

We present a semantics for strong negation systems on the basis of the subformula property of the sequent calculus. The new models, called subformula models, are constructed as a special class of canonical Kripke models for providing the way from the cut-elimination theorem to model-theoretic results. This semantics is more intuitive than the standard Kripke semantics for strong negation systems.

Paraconsistent Before-After Relation Reasoning Based on EVALPSN

A paraconsistent annotated logic program called EVALPSN by Nakamatsu has been applied to deal with real-time safety verification and control such as pipeline process safety verification and control. In this paper, we introduce a new interpretation for EVALPSN to dynamically deal with before-after relations between two processes (time intervals) in a paraconsistent way, which is named bf-EVALPSN. We show a simple example of an EVALPSN based reasoning system that can reason before-after relations in real-time.

Tableaux for Logic Programming with Strong Negation

Logic programming with strong negation (LPS) was proposed by Pearce and Wagner (1991) to handle both explicit and implicit negative information in knowledge representation in AI. We describe tableau calculi for LPS and establish the completeness. The proposed tableau calculi can deal with a wider class of programs in LPS. We also discuss possible refinements of the tableau calculi to improve efficiency.

Curry's paradox in contractionless constructive logic

We propose contractionless constructive logic which is obtained from Nelsons constructive logic by deleting contractions. We discuss the consistency of a naive set theory based on the proposed logic in relation to Currys paradox. The philosophical significance of contractionless constructive logic is also argued in comparison with Fitchs and Prawitzs systems.

An intelligent safety verification based on a paraconsistent logic program

We introduce an intelligent safety verification method based on a paraconsistent logic program EVALPSN with a simple example for brewery pipeline valve control. The safety verification is carried out by paraconsistent logic programming called EVALPSN.

Paraconsistent Annotated Logic Program EVALPSN and Its Applications

The main purpose of paraconsistent logic is to deal with inconsistency in a framework for consistent logical systems. It has been almost six decades since the first paraconsistent logical system was proposed by [13]. It was four decades later that a family of paraconsistent logic called ‘annotated logics’ was proposed by [6,51]. It can deal with inconsistency by introducing many truth values called ‘annotations’ that should be attached to each atomic formula, although their semantics is basically two-valued.

NELSON'S PARACONSISTENT LOGICS

. David Nelson’s constructive logics with strong negation may be viewed as alternative paraconsistent logic. These logics have been developed before da Costa’s works. We address some philosophical aspects of Nelson’s logics and give technical results concerning Kripke models and tableau calculi. We also suggest possible applications of paraconsistent constructive logics.

An Algebraic Version of the Monadic System C1

In this paper we present an algebraic version of the monadic system C1* of Da Costa [6] by using the concept of Curry Algebra [4]. The algebraic structure obtained is called Curry Algebra C1*. Some basic properties are discussed and presented.

A proof method for the six-valued logic for incomplete information

O. Garcia and M. Moussavi (1990) proposed a six-valued logic to model incomplete information. Although their logic is promising, it lacks a proof theory to serve as a basis for automated reasoning. We describe a sequent style proof method for the logic and show that the consequence relation in the logic is equivalent to the one by N.D. Belnaps (1977) four-valued logic. We also suggest alternative formal interpretations for the logic.