Wydawnictwo Uniwersytetu Łódzkiego,
Adam Kolany,
Miroslaw Wrobel,
adam.kolany@sonovum.de,
more

Progress in the medical diagnostic is relentlessly pushing the measurement technology as well with its intertwined mathematical models and solutions. Mathematics has applications to many problems that are vital to human health but not for all. In this article we describe how the mathematics of acoustocerebrography has become one of the most important applications of mathematics to the problems of...

Wydawnictwo Uniwersytetu Łódzkiego,
Jan von Plato,
Department of Philosophy University of Helsinki,
jan.vonplato@helsinki.fi

The way from linearly written derivations in natural deduction, introduced by Jaskowski and often used in textbooks, is a straightforward root-first translation. The other direction, instead, is tricky, because of the partially ordered assumption formulas in a tree that can get closed by the end of a derivation. An algorithm is defined that operates alternatively from the leaves and root of a derivation...

Wydawnictwo Uniwersytetu Łódzkiego,
Janusz Czelakowski,
Institute of Mathematics ans Informarics Opole University,
jczel@math.uni.opole.pl

The paper concerns the algebraic structure of the set of cumulative distribution functions as well as the relationship between the resulting algebra and the infinite-valued Łukasiewicz algebra. The paper also discusses interrelations holding between the logical systems determined by the above algebras.

Wydawnictwo Uniwersytetu Łódzkiego,
Alexander S Karpenko,
Department of Logic Russian Academy of Sciences,
as.karpenko@gmail.com

The paper discusses functional properties of some four-valued logics which are the expansions of four-valued Belnap’s logic DM4. At first, we consider the logics with two designated values, and then logics defined by matrices having the same underlying algebra, but with a different choice of designated values, i.e. with one designated value. In the preceding literature both approaches were developed...

Wydawnictwo Uniwersytetu Łódzkiego,
Wojciech Buszkowski,
Faculty of Mathematics and Computer Science Adam Mickiewicz University,
buszko@amu.edu.pl

In [5] we study Nonassociative Lambek Calculus (NL) augmented with De Morgan negation, satisfying the double negation and contraposition laws. This logic, introduced by de Grooté and Lamarche [10], is called Classical Non-Associative Lambek Calculus (CNL). Here we study a weaker logic InNL, i.e. NL with two involutive negations. We present a one-sided sequent system for InNL, admitting cut elimination...

Wydawnictwo Uniwersytetu Łódzkiego,
Janusz Ciuciura,
University of Lódź Department of Logic and Methodology of Science,
janciu@uni.lodz.pl

In 1953, Jerzy Kalinowski published his paper on the logic of normative sentences. The paper is recognized as one of the first publications on the formal system of deontic logic. The aim of this paper is to present a tableau system for Kalinowski’s deontic logic and to discuss some of the topics related to the paradoxes of deontic logic.

Wydawnictwo Uniwersytetu Łódzkiego,
Marek Nowak,
University of Lodz
Lindleya 3/5 Department of Logic,
marnowak@filozof.uni.lodz.pl

In the paper, tracing the traditional Hilbert-style syntactic account of logics, a syntactic characteristic of a closure operation defined on a complete lattice follows. The approach is based on observation that the role of rule of inference for a given consequence operation may be played by an ordinary binary relation on the complete lattice on which the closure operation is defined.

Wydawnictwo Uniwersytetu Łódzkiego,
María Manzano,
Manuel Crescencio Moreno,
University of Salamanca Department of Philosophy,
more

This article is an extended promenade strolling along the winding roads of identity, equality, nameability and completeness, looking for places where they converge. We have distinguished between identity and equality; the first is a binary relation between objects while the second is a symbolic relation between terms. Owing to the central role the notion of identity plays in logic, you can be interested...

Wydawnictwo Uniwersytetu Łódzkiego,
Tomasz Jarmużek,
Mateusz Klonowski,
Jacek Malinowski,
more

We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w , where w is a probability function on a Boolean language. A |≈w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the intersection of |≈w , for all w, and give some formal...

Wydawnictwo Uniwersytetu Łódzkiego,
Krystyna Mruczek-Nasieniewska,
Marek Nasieniewski,
Nicolaus Copernicus University in Toruń,
more

In [1] J.-Y. Bèziau formulated a logic called Z. Bèziau’s idea was generalized independently in [6] and [7]. A family of logics to which Z belongs is denoted in [7] by K. In particular; it has been shown in [6] and [7] that there is a correspondence between normal modal logics and logics from the class K. Similar; but only partial results has been obtained also for regular logics (see [8] and [9])...

Wydawnictwo Uniwersytetu Łódzkiego,
Andrzej Pietruszczak,
ul. Moniuszki 16 Nicolaus Copernicus University in Toruń,
Andrzej.Pietruszczak@umk.pl

This is the second, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics can be divided into certain groups. Each such group depends only on which of the following formulas are theses of all logics from this group: (N), (T), (D), ⌜(T)∨☐q⌝, and for any n 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and...

Wydawnictwo Uniwersytetu Łódzkiego,
Zalán Gyenis,
Jagiellonian University Department of Logic,
gyz@renyi.hu

The sole purpose of this paper is to give an algebraic characterization, in terms of a superamalgamation property, of a local version of Craig interpolation theorem that has been introduced and studied in earlier papers. We continue ongoing research in abstract algebraic logic and use the framework developed by Andréka– Németi and Sain.

Wydawnictwo Uniwersytetu Łódzkiego,
Vincent Degauquier,
University of Namur Espace philosophique de Namur,
vincent.degauquier@gmail.com

The temporal logic KtT4 is the modal logic obtained from the minimal temporal logic Kt by requiring the accessibility relation to be reflexive (which corresponds to the axiom T) and transitive (which corresponds to the axiom 4). This article aims, firstly, at providing both a model-theoretic and a proof-theoretic characterisation of a four-valued extension of the temporal logic KtT4 and, secondly,...

Wydawnictwo Uniwersytetu Łódzkiego,
Guillermo Badia,
Johannes Kepler Universität Department of Knowledge-Based Mathematical Systems,
guillermo.badia_hernandez@jku.at

We characterize the non-trivial substructural logics having the variable sharing property as well as its strong version. To this end, we find the algebraic counterparts over varieties of these logical properties.

Wydawnictwo Uniwersytetu Łódzkiego,
Michał M Stronkowski,
Warsaw University of Technology Faculty of Mathematics and Information Science,
m.stronkowski@mini.pw.edu.pl

We provide simple algebraic proofs of two important facts, due to Zakharyaschev and Esakia, about Grzegorczyk algebras.

Wydawnictwo Uniwersytetu Łódzkiego,
Mirjana Ilić,
Faculty of Economics University of Belgrade,
mirjanailic@ekof.bg.ac.rs

A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The operational rules of NI are obtained by the translation from Gentzen’s calculus LJ and the normalization is proved, via translations from sequent calculus derivations to natural deduction derivations and back.

Wydawnictwo Uniwersytetu Łódzkiego,
Young Bae Jun,
Eun Hwan Roh,
Seok Zun Song,
more

The notions of a C-energetic subset and (anti) permeable C-value in BCK-algebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an (anti) permeable C-value are provided. Also conditions for a subset to be a C-energetic subset are discussed. We decompose BCK-algebra by a partition which consists of a C-energetic subset and a commutative ideal.

Wydawnictwo Uniwersytetu Łódzkiego,
George Tourlakis,
janciu@uni.lodz.pl

Reference [12] introduced a novel formula to formula translation tool (“formulators”) that enables syntactic metatheoretical investigations of first-order modal logics, bypassing a need to convert them first into Gentzen style logics in order to rely on cut elimination and the subformula property. In fact, the formulator tool, as was already demonstrated in loc. cit., is applicable even to the metatheoretical...

Uniwersytet Łódzki. Katedra Logiki i Metodologii Nauk,
Fernando Ferreira,
Gilda Ferreira,
Universidade de Lisboa,
more

We give an elementary proof (in the sense that it is formalizable in Peano arithmetic)
of the strong normalization of the atomic polymorphic calculus F_{at} (a
predicative restriction of Girard’s system F).

Wydawnictwo Uniwersytetu Łódzkiego,
Fernando Ferreira,
Gilda Ferreira,
Faculdade de Ciências Universidade de Lisboa,
more

We give an elementary proof (in the sense that it is formalizable in Peano arithmetic) of the strong normalization of the atomic polymorphic calculus Fₐₜ (a predicative restriction of Girard’s system F).