
Authors:
Krister SEGERBERG
Title:A general framework for the logic of theory change
Pages:28
File:bibtex
Abstract ( + )
That the logic of theory of change can be related to dynamic modal logic has been recognized by authors like van Benthem, Fuhrmann and, especially, by de Rijke. Here we try to take that insight further. Dynamic doxastic logic concerns an agent who inhabits a world and is able to form theories about it. In particular there are three types of doxastic action of which he is capable: expanding his beliefs by accepting a proposition A without modifying the resulting set of beliefs; revising his beliefs by accepting a proposition φ and modifying the resulting set of beliefs; and contracting his beliefs by giving up a proposition φ and modifying the resulting set of beliefs. We use de Rijke's symbolism +&phi for expansion by φ, *φ for revision by φ, and φ for contraction by φ.

Authors:
Konrad TURZYNSKI
Title:Simple sandwiches and related results of Keisler and Kochen
Pages:914
File:bibtex
Abstract ( + )
The paper is a more detailed abstract of the first part of the paper presented on the XXXVIII Conference on the History of Logic held in Cracow (November 1718, 1992) and published in Studia Logica. Its aim is a further simplification of known theorems due to H.J.Keisler and S.B.Kochen. All these results determine relations between sentences, containing in their prenex normal form a given number of alternations of quantifiers, and some modeltheoretic constructions called sandwiches.

Authors:
Roman TUZIAK
Title:Paraconsistent extensions of positive logic
Pages:1520
File:bibtex
Abstract ( + )
In this paper we are interested in various negation operations (we shall call them paraconsistent negations) that lead to paraconsistent results. In other words: Positive (negationfree) Logic (abbreviated to POS) furnished with a negation of this kind is supposed to be paraconsistent, that is, it should not contain "A implies (not A implies B)" as a theorem. All the other connectives (conditional, biconditional, disjunction, and conjunction) are classical.

Authors:
NobuYuki SUZUKI
Title:A remark on the delta operation and the Kripke sheaf semantics in superintuitionistic predicate logic
Pages:2128
File:bibtex
Abstract ( + )
The delta operation is originally defined on the set of all superintuitionistic propositional logics, and can easily be extended to an operation on the set of all superintuitionistic predicate logics (cf. paper by Komori). We show that every superintuitionistic predicate logic L satisfying Δ(L)=L has the disjunction and existence properties and moreover the same propositional fragment as the intuitionistic logic H. We use the Kripke sheaf semantics which is introduced by ShehtmanSkvortsov. In this setting, we can generalize ideas in Komori, Minari and Nakamura quite naturally. We present infinitely many examples of fixed points of Δ. In the following, we will deal with superintuitionistic propositional and predicate logics. Hence we will omit the adjective ``superintuitionistic''.

Authors:
Istvan NEMETI
Title:Ontology can turn negative results to positive
Pages:2940
File:bibtex
Abstract ( + )
Here we discuss four seemingly different problem areas which turn out to be strongly related. These are: (1) The finite variable fragment Ln of first order logic with equality. (2) The finitization problem of algebraic logic, cf. papers by Nemeti, Sain, HenkinMonk, Monk . (3) Propositional multimodal logic equivalent with classical first order logic (modal logics of quantification and substitution). (4) Untyped higherorder logic. The ZFC versions of all four of these areas are almost ``dominated'' by negative results. We will see that this picture changes for the better if we switch to a certain nonwellfounded set theory (see below for definitions) as our foundation of mathematics. At the end, we will look into the natural question of how much nonwellfoundedness is needed i.e., how much of it is needed. We will see that the answer is ``not much'', at least in a sense.

Authors:
Wendy MacCAULL
Title:Kripke semantics for logic with BCK
Pages:4151
File:bibtex
Abstract ( + )
We present Kripke semantics for some substructural logics with weakening, known as logics with BCK implication. This work is a continuation of the work of Allwein and Dunn on Kripke semantics for Linear Logic, which in turn rested on Dunn's Gaggle Theory and on Urquhart's Representation Theory for nondistributive lattices. The basic idea in the representation theory is to use maximally disjoint filterideal pairs (maximal pairs) to separate distinct elements. A collection of subsets of the set of maximal pairs forms the representation lattice. Ternary relations are defined on the set of maximal pairs which embody properties of the operations "&" and "supset". A three way valuation of formulas gives rise to a definition of canonical Kripke model. Properties of the ternary relations on the set of maximal pairs are used in the abstract definition of Kripke semantics. Soundness and strong completeness hold.

Authors:
Alexander S. KARPENKO
Title:The class of precomplete Lukasiewicz's manyvalued logics and the law of prime numbers generation
Pages:5257
File:bibtex
Abstract ( + )
A propositional formula (a function) whose iteration generates classes of prime numbers has been found. Some properties of these classes are discussed in the paper.

Authors:
Tomasz KOWALSKI
Title:A Perzanowski's hypothesis confirmed
Pages:5859
File:bibtex
Abstract ( + )
Jerzy Perzanowski has put forward the hypothesis that the normal modal logic KP, called by him: the logic of parasymmetry, and defined as the Kripke logic K plus the axiom "L(A implies LA) iff L(MA implies A)", coincides with the system K4LB, i.e. K plus axioms "LA implies LLA", and "L(A implies LMA)". Moreover, Perzanowski has shown that the hypothesis in question is equivalent to the fact that "L(A implies LMA)" is a thesis of KP. We will present a proof of the latter statement, confirming thereby the hypothesis. In what follows a basic knowledge of normal modal logics and normal modal algebrasis assumed.

Authors:
Heinrich WANSING
Title:A new axiomatization of K_{1}
Pages:6062
File:bibtex
Abstract ( + )
Paper presents another axiomatization of the smallest normal propositional tense logic K_{1}. This axiomatization is extracted from a certain cutfree proof of the K axiom schema in the modal display calculus.