
Authors:
Janis CIRULIS
Title:Orthoposets with Quantifiers
Pages:112
File:bibtex
Abstract ( + )
A quantifier on an orthoposet is a closure operator whose range is closed under orthocomplementation and is therefore a suborthoposet. There is a natural bijective connection between quantifiers and their ranges. We extend it to a bijective connection between certain families of quantifiers on an orthoposet and certain families of its suborthoposets.

Authors:
Dolph ULRICH
Title:Single Axiom for Relevant Implication
Pages:1316
File:bibtex
Abstract ( + )
R is shown to be a single axiom for the implicational fragment R_{→} of that system.

Authors:
Rodolfo C. Ertola BIRABEN
Title:On Some Extensions of Intuitionistic Logic
Pages:1722
File:bibtex
Abstract ( + )
We prove that many extensions of Intuitionistic Sentential Calculus ISC with new intuitionistic connectives that are known to be conservative extensions of ISC are not conservative extensions of Intuitionistic Predicate Calculus because formulas such as Kuroda's are derivable. We thus solve a problem posed by LópezEscobar in 1985 and answer a question posed by Humberstone in 2001 regarding a connective called the strongest anticipator.

Authors:
Zofia KOSTRZYCKA
Title:On Interpolation and HalldenCompleteness in NEXT(KTB)
Pages:2332
File:bibtex
Abstract ( + )
The Craig interpolation property and Halldencompleteness are considered in the case of the logics from NEXT(KTB), where KTB is the socalled Brouwerian modal logic.

Authors:
Andrzej PIETRUSZCZAK
Title:Semantical Investigations on Some Weak Modal Logics. Part I
Pages:3350
File:bibtex
Abstract ( + )
In this paper we examine weak logics similar to S0.5[□Φ], where Φ⊆ S0.5. We also examine their versions (one of which is S0.5_{rte}[□Φ] ) that are closed under replacement of tautological equivalents (rte). We have that: S0.5_{rte}[□(K),□(T)]⊊ S0.9, S0.5_{rte}[□(X),□(T)]⊊ S1, and in general, if Φ⊆ E1, then S0.5_{rte}[□Φ]⊊S2. In the second part we shall give simplified semantics for these logics, formulated by means of some Kripkestyle models. We shall also prove that the logics in question are determined by some classes of these models.

Authors:
Gemma ROBLES
Title:A Semantical Proof of the Admissibility of the Rule Assertion in Some Relevant and Modal Logics
Pages:5160
File:bibtex
Abstract ( + )
It is proved that the rule assertion is admissible in some relevant and modal logics sound and complete in respect of ternary relational models of a certain type

Authors:
Szymon Frankowski
Title:Triconsequences
Pages:6170
File:bibtex
Abstract ( + )
In [3] the notion of biconsequence has been presented. It can be seen as a disjoint sum (union) of consequence and pconsequence operations. However, it is possible to construct disjoint unions of q, p and ordinary consequence at the same time. Such an operation will be called triconsequence in this paper.

Authors:
A. V. FIGALLO and G. PELAITAY
Title:Remarks on Heyting Algebras with Tense Operators
Pages:7174
File:bibtex
Abstract ( + )
The concept of tense operators on Heyting algebras was introduced in [3]. The aim of this paper is to prove, that the set of axioms proposed by I. Chajda in [3, Definition 1], is a dependent axioms system and show that tense operators F and P can not be regarded as existential quantifiers.

Authors:
Katsumi SASAKI
Title:Transitivity of Finite Models Constructed from Normal Forms for a Modal Logic Containing K4
Pages:7588
File:bibtex
Abstract ( + )
By using normal forms for a modal logic L, Moss [3] constructed finite model C_{n,m}(L) and proved that the model is reflexive if L contains KT, it is serial if L contains KD, and so on. However, concerning to transitivity, he raised the problem: ``Is it true that for every logic L containing K4, C_{n,m}(L) is transitive for almost all n?''. In the present paper, by using another type of normal forms in [4], we prove that the model C_{n,m}(S4BW_{2}) is not transitive for each n ≥ 2, where S4BW_{2} is the logic characterized by the class of the reflexive and transitive models of width ≤ 2.

Authors:
Andrzej INDRZEJCZAK
Title:CutFree Hypersequent Calculus for S4.3.
Pages:89104
File:bibtex
Abstract ( + )
Hypersequent calculi (HC) are the generalization of ordinary sequent calculi obtained by operating with sets of sequents instead of single sequents. HC, introduced independently by Pottinger and Avron, proved to be very useful in the field of nonclassical logics. Nevertheless their application to modal logics was rather limited. We provide a cutfree hypersequent calculus HCS4.3 for modal logic of linear frames based on the idea of hypersequent formalization for GödelDummett's logic due to Avron. Also a variant of HCS4.3 with analytic cut but with nonbranching logical rules is presented.