
Authors:
Kosta DOSEN
Title:Cut elimination in adjunction
Pages:6173
File:bibtex
Abstract ( + )
The notion of adjunction is formulated so that for every arrow in freely generated adjunctions there is a compositionfree term for this arrow, which can be brought into a normal form unique for the arrow. In this formulation, natural transformations are not conceived as families of arrows, but as operations on arrows. Composition elimination is the form Gentzen's cut elimination takes in categories. The compositionfree normal form serves to obtain simple geometrical decision procedures for the commuting of diagrams. It serves also to show that adding to the notion of adjunction any new equality between arrows in the language of free adjunctions would trivialize this notion.

Authors:
Tadao ISHII
Title:A note on varieties of PCIalgebras with EDPC
Pages:7581
File:bibtex
Abstract ( + )
We will formulate a necessary and sufficient condition for a variety of PCIalgebras to have EDPC. R. Suszko proposed the sentential calculus with identity. PCI is a formalization of modal logic K in the SCI language, for which PCIalgebras provide an algebraic semantics.

Authors:
Misao NAGAYAMA
Title:A normalization theorem for PW
Pages:8388
File:bibtex
Abstract ( + )
In this note, we consider sequent calculus for an implicational noncommutative intuitionistic logic PW, or equivalently called BB'I. We shall prove the Normalization theorem for L_{BB'I}, which Komori used in his syntactic proof of Martin's theorem, known as a solution to the PW problem.

Authors:
JeanYves BEZIAU
Title:A sequent calculus Lukasiewicz's threevalued logic based on Suszko's bivalent semantics
Pages:8997
File:bibtex
Abstract ( + )
A sequent calculus S3 for Lukasiewicz's logic L3 is presented. The completeness theorem is proved relatively to a bivalent semantics equivalent to the non truthfunctional bivalent semantics for L3 proposed by Suszko in 1975. A distinguishing property of the approach proposed here is that we are keeping the format of the classical sequent calculus as much as possible.

Authors:
Ivo DUNTSCH and Ewa ORLOWSKA
Title:Mixing modal and sufficiency operators
Pages:99107
File:bibtex
Abstract ( + )
We explore Boolean algebras with sufficiency operators, and investigate a class of mixed algebras which corresponds to frames < U,R > with a modal operator < R > and a sufficiency operator [[R]].

Authors:
NobuYuki SUZUKI
Title:A remark on superintuitionistic predicate logics having the same propositional fragment
Pages:107115
File:bibtex
Abstract ( + )
We make a remark on the lattice structure of the set of superintuitionistic predicate logics having the same propositional fragment. We present linearly ordered intervals consisting of finitely many logics at the upper part of the set of predicate logics whose propositional fragment is the second greatest intermediate propositional logic.