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#### Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

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 ...

#### Some Weak Variants of the Existence and Disjunction Properties in Intermediate Predicate Logics

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

We discuss relationships among the existence property, the disjunction property, and their weak variants in the setting of intermediate predicate logics. We deal with the weak and sentential existence properties, and the ...

#### Cut Elimination Theorem for Non-Commutative Hypersequent Calculus

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

Hypersequent calculi (HC) can formalize various non-classical logics. In [9] we presented a non-commutative variant of HC for the weakest temporal logic of linear frames Kt4.3 and some its extensions for dense and serial ...

#### On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only ...

#### Universality of Logic

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

This paper deals with the problem of universality property of logic. At first, this property is analyzed in the context of first-order logic. Three senses of the universality property are distinguished: universal applicability, ...

#### The Infinite-Valued Łukasiewicz Logic and Probability

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

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 ...

#### Four-Valued Logics BD and DM4: Expansions

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

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 ...

#### Three Doctrines of the Nature of Mathematics (Some Comments of a Knowledge Theorist)

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

In this note I am reflecting on interrelations between three concepts of truth: (1) that employed by Hilbert arguing his formalist view on the nature of mathematics, (2) Freges idea of truth supported by mathematical ...

#### From Gentzen to Jaskowski and Back: Algorithmic Translation of Derivations Between the Two Main Systems of Natural Deduction

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

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 ...

#### Identity, Equality, Nameability and Completeness

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)

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 ...