File  
language 
eng

Author 
Kondo, Michiro

Description  In our usual logic, we do not infer arbitrary proposition from a contradictory one. Also in executing programs, there is a state that a proposition A holds in some program and in another there is a state in which A does not hold. To explain these situations, recently, the logic called paraconsistent is proposed and investigated. ([1, 2, 3] etc.) Since the logic has two kinds of negation operators, there are cases such that both A and not A are theorems and hence it is difficult to obtain the concept of truth. To the contrary, De Glas has proposed in [4] a pseudoconsistent logic (PCL) in which AΛ～ A → ⊥ is not a theorem but so ～ (AΛ ～ A) is. He also gave the axiomatization of PCL and proved the completeness theorem by two kinds of models, PCmodels and Imodels. These models are based on PCalgebras and partially ordered sets, respectively.
But there is an important question which is not referred : Is the logic PCL decidable ? In the present paper we prove the decidabily of PCL according to the following steps: 1. PCL is characterized by the the class of preordered sets instead of that of partially ordered sets, that is ├_PCL A ⇔ A : POvalid; 2. TL is characterized by the class of some kinds of Kripketype models, that is, ├_TL A ⇔ A : TLvalid; 3. PCL can be embedded into a certain tense logic (TL), that is, for some map ε, A : POvalid ⇔ ε(A) : TLvalid; 4. TL is decidable and hence so PCL is. 
Subject  Pseudoconsistent Logic
Tense Logic

Journal Title 
島根大学総合理工学部紀要. シリーズB

Volume  33

Start Page  21

End Page  30

ISSN  13427121

Published Date  200003

NCID  AA11157123

Publisher  島根大学総合理工学部

NII Type 
Departmental Bulletin Paper

Format 
PDF

Text Version 
出版社版

OAIPMH Set 
Interdisciplinary Graduate School of Science and Engineering
