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Now showing items 1-10 of 18

#### An Alternative Natural Deduction for the Intuitionistic Propositional Logic

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

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 ...

#### Commutative Energetic Subsets of BCK-Algebras

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

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. ...

#### Elementary Proof of Strong Normalization for Atomic F

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

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).

#### Some Algebraic and Algorithmic Problems in Acoustocerebrography

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

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 ...

#### Simple Decision Procedure for S5 in Standard Cut-Free Sequent Calculus

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

In the paper a decision procedure for S5 is presented which uses a cut-free sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to ...

#### A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. ...

#### Categorical Abstract Logic: Hidden Multi-Sorted Logics as Multi-Term Institutions

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

Babenyshev and Martins proved that two hidden multi-sorted deductive systems are deductively equivalent if and only if there exists an isomorphism between their corresponding lattices of theories that commutes with ...

#### Quasiorders, Tolerance Relations and Corresponding “Partitions”

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

The paper deals with a generalization of the notion of partition for wider classes of binary relations than equivalences: for quasiorders and tolerance relations. The counterpart of partition for the quasiorders is based ...

#### Axiomatization of a Basic Logic of Logical Bilattices

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

A sequential axiomatization is given for the 16-valued logic that has been proposed by Shramko-Wansing (J Philos Logic 34:121–153, 2005) as a candidate for the basic logic of logical bilattices.

#### A New Arithmetically Incomplete First- Order Extension of Gl All Theorems of Which Have Cut Free Proofs

(Wydawnictwo Uniwersytetu Łódzkiego, 2016)

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 ...