Papers by Zofia Kostrzycka
Journal of Logic and Computation, Jun 26, 2009
For the given logical calculus we investigate the size of the fraction of true formulas of a cert... more For the given logical calculus we investigate the size of the fraction of true formulas of a certain length n against the number of all formulas of this length. We are especially interested in asymptotic behaviour of this fraction when n tends to infinity. If the limit of the fraction exists it represents a number which we call the density of truth for the investigated logic. In this paper we apply this approach to the Dummett intermediate linear logic (see [2]). This paper shows the exact density of this logic and demonstrates that it covers a substantial part of classical propositional calculus. In fact, despite strictly mathematical means used to solve all discussed problems, this paper may have a philosophical impact on understanding to what extent the phenomenon of truth is sporadic or frequent in random mathematics sentences.
2022 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
Journal of Logic and Computation, 2021
We prove that $\textbf {K4}^{\textbf {n+}}\textbf {B}^{\textbf {k+}}$ has projective unification,... more We prove that $\textbf {K4}^{\textbf {n+}}\textbf {B}^{\textbf {k+}}$ has projective unification, for any $k,n\geq 1$. It means, in particular, that any weakly transitive and weakly symmetric modal logic is unitary. Some consequences of projective unification concerning structural completeness and passive rules are provided.
In this paper the equivalential reducts of classical and intuitionistic logics over language with... more In this paper the equivalential reducts of classical and intuitionistic logics over language with two propositional variables are characterized. Next, the size of the fraction of tautologies of these logics against all formulas are investigated. To do that quite non-logical methods are used. 1
In this paper we examine normal extensions of Grzegorczyk’s logic over language with one proposit... more In this paper we examine normal extensions of Grzegorczyk’s logic over language with one propositional variable and signs of {→,¤} only. 1 Grzegorczyk’s logic and its normal extensions Syntactically, Grzegorczyk’s logic Grz is characterized as a normal extension of S4 modal calculus by the axiom (grz) ¤(¤(p → ¤p) → p) → p The set of rules consists of modus ponens, substitution and necessitation. Semantically, Grz logic is characterized by the class of finite reflexive and tran-sitive trees. Recall, that by a tree we mean a rooted frame F =< W,R> such that for every point x ∈W, the set x ↓ is finite and linearly ordered by R. In this section we examine normal extensions of Grzegorczyk’s logic obtained by adding to the set of axioms new formulas. The axiomatic extensions are uniformly connected with a depth of a tree. Definition 1. A frame F is of depth n < ω if there is a chain of n points in F and no chain of more than n points exists in F. For n> 0, let Jn be an axiom s...
Discrete Mathematics & Theoretical Computer Science, 2006
International audience The aim of this paper is counting the probability that a random modal form... more International audience The aim of this paper is counting the probability that a random modal formula is a tautology. We examine $\{ \to,\Box \}$ fragment of two modal logics $\mathbf{S5}$ and $\mathbf{S4}$ over the language with one propositional variable. Any modal formula written in such a language may be interpreted as a unary binary tree. As it is known, there are finitely many different formulas written in one variable in the logic $\mathbf{S5}$ and this is the key to count the proportion of tautologies of $\mathbf{S5}$ among all formulas. Although the logic $\mathbf{S4}$ does not have this property, there exist its normal extensions having finitely many non-equivalent formulas.
Bulletin of the Section of Logic, 2016
The Craig interpolation property and interpolation property for deducibility are considered for s... more The Craig interpolation property and interpolation property for deducibility are considered for special kind of normal extensions of the Brouwer logic.
Scientific Issues Jan Długosz University in Częstochowa. Mathematics, 2016
Bulletin of the Section of Logic
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Bulletin of the Section of Logic
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Mathematical Logic Quarterly, 2014
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MLQ, 2008
In this paper we construct a continuum of logics, extensions of the modal logic T2 = KTB ⊕ 2 2 p ... more In this paper we construct a continuum of logics, extensions of the modal logic T2 = KTB ⊕ 2 2 p → 2 3 p, which are non-compact (relative to Kripke frames) and hence Kripke incomplete.
Journal of Logic, Language and Information, 2007
This paper is an attempt to count the proportion of tautologies of some intermediate logics among... more This paper is an attempt to count the proportion of tautologies of some intermediate logics among all formulas. Our interest concentrates especially on Dummett's and Medvedev's logics and their {→, ∨, ¬} fragments over language with one propositional variable.
Journal of Logic and Computation, 2009
ABSTRACT
For the given logical calculus we investigate the size of the fraction of true formulas of a cert... more For the given logical calculus we investigate the size of the fraction of true formulas of a certain length n against the number of all formulas of such length. We are especially interested in asymptotic behaviour of this fraction when n tends to inflnity. If the limit of the fraction exists it repre- sents a number which we may call
Abstract. We study normal extensions of the modal Brouwer logic KTB which have nice semantical ch... more Abstract. We study normal extensions of the modal Brouwer logic KTB which have nice semantical characterization. They are logics deter-mined by nets of clusters with bounded number of branching. It occurred that the studied logics are Kripke complete and have finite model prop-erty. Then we investigate the logics with respect to interpolation. It is known that the logics KTB has interpolation. We prove that there are very few locally finite logics within the family of NEXT (KTB) with interpolation. We continue research on Brouwerian modal logics having Craig interpolation property. In paper [2] we describe two-step transitive Brouwerian modal logics without interpolation. Now, we study Brouwerian logics not being n-transitive at all with respect to the interpolation property. We examine the Brouwer modal logic KTB and its normal extensions, which are determined by a class of Kripke frames equipped with a tolerance relation and having special forms. Each reflexive and symmetric Kripk...
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Papers by Zofia Kostrzycka