
Authors:
Andrzej PIETRUSZCZAK
Title:Semantical Investigations on Some Weak Modal Logics. Part II
Pages:109130
File:bibtex
Abstract ( + )
In both parts of 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 present part we give simplified semantics for these logics, formulated by means of some Kripkestyle models. We prove that the logics in question are determined by some classes of these models.

Authors:
M. Sambasiva Rao
Title:Normal Filters of Distributive Lattices
Pages:131143
File:bibtex
Abstract ( + )
The concepts of normal filters and normlets are introduced in a distributive lattice. The class of quasicomplemented lattices are characterized with the help of normlets. Normal filters are also characterized in terms of normlets. Disjunctive lattices are characterized in terms of normal filters. Finally, some properties of the space of prime normal filters are studied in topological sense.

Authors:
Zdzislaw DYWAN
Title:A Matrix Criterion of Hallden Completeness
Pages:145148
File:bibtex
Abstract ( + )
This paper presents a matrix criterion of Hallden completeness for logics which are extensions of classical logic, e.g. modal logics.

Authors:
Zdzislaw DYWAN
Title:A Simple Axiomatization of Lukasiewicz's Modal Logic
Pages:149153
File:bibtex
Abstract ( + )
We will propose a new axiomatization of fourvalued Lukasiewicz's modal logic in the version with rejection. Moreover, two controversies connected with violation of fundamental intuitions about necessity are discussed and an argumentation against suitability of this logic for analysis of Aristotle's modal syllogistic is given.

Authors:
Michal ZAWIDZKI
Title:Adequacy of the Logic K(E_{n})
Pages:155172
File:bibtex
Abstract ( + )
In this paper we characterize syntax and semantics of the logic K(E_{n})  modal logic with global counting operators E_{>n} E_{=n} and E_{>}. We fill the gap announced in [1] by providing the axiomatization of this logic. Taking advantage of the combinatorial parts of completeness proofs for graded modal logics to be found in [4] and [6], we show that K(E_{n}) is strongly adequate with respect to the class of all frames F=< W, R_{◊}>.

Authors:
Francois LEPAGE
Title:Partial Probability Functions and Intuitionistic Logic
Pages:173184
File:bibtex
Abstract ( + )
We first present a sound and complete system of intuitionistic logic augmented with Nelson's strong negation and interpreted in Kripke's models' structure. Then, we show that intuitionistic logic can naturally be interpreted in a modal trivalent logic (propositions are true, false or undefined). Secondly, we introduce a partial probability interpretation, which is inspired by Popper's conditional probability functions and are characterized by the fact that conditions are not propositions but rather sets of propositions. Finally, we define the notion of probabilistic validity and we show using Kripke's models that the intuitionistic system is sound and complete.

Authors:
Malgorzata KRUSZELNICKA
Title:A Note on Bisimulations of Finite Kripke Models
Pages:185198
File:bibtex
Abstract ( + )
In our paper we consider the notion of bounded bisimulation of Kripke models for intuitionistic firstorder theories. As it is already known, in this case, the existence of bisimulation between given two Kripke models implies their logical equivalence. We present a new result which states that, under some additional conditions, for every two firstorder Kripke models that are equivalent, there is a bisimulation between them.

Authors:
Sergei P. ODINTSOV
Title:On Deductive Bases for Partial Equilibrium Logic
Pages:199213
File:bibtex
Abstract ( + )

Authors:
Marek NASIENIEWSKI and Andrzej PIETRUSZCZAK
Title:On the Weakest Modal Logics Defining Jaskowski's Logic D_{2} and the D_{2}Consequence
Pages:215232
File:bibtex
Abstract ( + )