
Authors:
Hirohiko KUSHIDA
Title:Applicability of Motohashi's Method to Modal Logics
Pages:121134
File:bibtex
Abstract ( + )
Motohashi showed that the intuitionistic predicate logics (with the constant domains and with increasing domains) can be faithfully embedded in the classical predicate logic by a prooftheoretic method. The embedding treated could be considered a combination of the modal embedding of intuitionistic logic in the modal logic S4 and the ``standard translation'' of S4 to classical predicate logic. By extending Motohashi's method, In the present paper, we show that Motohashi's method can be applied to a wide range of modal predicate logics. We prove correspondence theorems based on the standard translation between classical predicate logic and the quantified versions of S4 and S5 and some subsystems of them, in a uniform way.

Authors:
Dolph ULRICH
Title:Dcomplete Axioms for the Classical Equivalential Calculus
Pages:135142
File:bibtex
Abstract ( + )
Virtually all previously known axiom sets for the classical equivalential calculus, EQ, are Dincomplete: not all theorems derivable by substitution and detachment can be derived using the rule D of condensed detachment alone. The only exception known to the author is Wajsberg's base {EEpEqrErEqp, EEEpppp}. This axiom set, albeit inorganic since one of its members contains a theorem of EQ as a proper subformula, is here shown to be Dcomplete. Dcomplete single axioms for EQ are then constructed, culminating with EEpqEErqEsEsEsEsEpr which has the distinction of being both Dcomplete and organic.

Authors:
Adam KOLANY
Title:Rado Selection Lemma and Other Combinatorial Statements Uniformly Proved
Pages:143149
File:bibtex
Abstract ( + )
We present an uniform method of proving some combinatorial statements of Rado Selection Lemma type. They mainly come from Cowen.

Authors:
Andrzej INDRZEJCZAK
Title:Sequent Calculi for Monotonic Modal Logics
Pages:151164
File:bibtex
Abstract ( + )
It is well known that the epistemic or doxastic interpretation of modal constants leads to unintuitive results in the context of normal logics. This is the main reason that weaker logics are considered as better candidates. One can easilly notice however, that investigations into proof methods and decision procedures for such logics are rather modest. There is a lot of books and papers devoted to exploration of nonaxiomatic formalizations of modal logic but, only Fitting covers some regular ones. Lavendhomme and Lucas offer cutfree sequent calculus only for the most basic classical and monotonic systems. In particular, the systems containing some axioms and have been of no special interest up to now, despite their importance in epistemic and doxastic logics. In what follows we offer an extension of work covering all combinations of axioms D, T, 4, B and 5 over the weakest monotonic logic M. Our approach to the logics is purely syntactical. First we present a class of sequent calculi that are equivalent to axiomatic formalizations of the logics we mentioned, and then show by standard Gentzen argument, that most of them are cutfree.

Authors:
Norihiro KAMIDE
Title:Cutfree Singlesuccedent Systems Revisited
Pages:165175
File:bibtex
Abstract ( + )
It is shown that LJ with a generalized Dummett rule, LJ with a generalized Peirce rule and LJ with a specialized Peirce rule have the cutelimination property. It is also shown that the third system has a weak subformula property and Craig's interpolation property. The systems presented are versions of singlesuccedent sequent systems for classical logic. The cutelimination results for the singlesuccedent systems can also be extended to modal logics.

Authors:
Gemma ROBLES, Francisco SALTO and Jose M. MENDEZ
Title:A Constructive Negation Defined with aNegation Connective for Logics Including Bp+
Pages:177189
File:bibtex
Abstract ( + )
The concept of constructive negation we refer to in this paper is (minimally) intuitionistic in character. The idea is to understand the negation of a proposition A as equivalent to A implying a falsity constant of some sort. Then, negation is introduced either by means of this falsity constant or, as in this paper, by means of a propositional connective defined with the constant. But, unlike intuitionisitc logic, the type of negation we develop here is, of course, devoid of paradoxes of relevance.