Japan Advanced Institute of Science and Technology
JAIST Repository
https://dspace.jaist.ac.jp/
Title
同一結合子を持つ非古典論理とその代数的特徴付けAuthor(s)
石井, 忠夫Citation
Issue Date
2000‑03Type
Thesis or DissertationText version
authorURL
http://hdl.handle.net/10119/898Rights
Description
Supervisor:小野 寛晰, 情報科学研究科, 博士algebraic characterization
Tadao ISHII,
School of Information Science, JAIST,
Tatsunokuchi,Ishikawa 923{1292, Japan
March 2000
Abstract
Inthisthesis,weinvestigatevariouskindsofnonclassicallogicsbythepropertyofidentity
connective. Around 1970, R. Suszkoproposed the sentential calculuswith identity (SCI
for short)to realize somephilosophical ideas of L.Wittgenstein's Tractatus. InSCI, be-
sidesthelogicalvalue,heformalizedthereferentofsentencesbyusingidentityconnective.
Inspired by his idea, we intro duce a weak system, i.e., propositional calculus with iden-
tity (PCI for short), whichis obtained from SCI by deleting twoaxioms which express
the reexivity and transitivity of identity. As an extension of the simulation property
of SCI, we reconstruct various kinds of nonclassical logics on PCI, including two typ es
of logics, namely classical logics with additional operators and weak logics with various
kindsof weakimplications,e.g., strict/relevance/linearimplication. Infact,inthis thesis
we show that the following logics can be translated tosome extensions of PCI; classical
modal logicsK,KT, KB,K4,KD, K5,S4 and S5with necessaryoperator
2
,Angell's
analytic containment logic AC with relevance entailment ;, Corsi's weak logic F with
strict implication *and Girard'sclassical linear logic GL with linear implication . In
particular, the modal logic Kis shown tobetranslated into anextensionPCI
K
of PCI.
Then wewill focus onthe algebraic property of PCI
K
-algebras, whichoerthe algebraic
semantics of extensions of PCI
K
. We will give a necessary and sucient condition for a
subvariety ofPCI
K
-algebras tohaveequationally denable principal congruences (EDPC
for short) property.
Keywords : EDPC, identity connective, nonclassical logic, non-Fregean logic,
SCI, Suszko, PCI
Copyrightc 2000byTadaoISHII
