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Now showing items 1-8 of 8

#### Rule-Generation Theorem and its Applications

(Wydawnictwo Uniwersytetu Łódzkiego, 2018)

In several applications of sequent calculi going beyond pure logic, an introduction of suitably defined rules seems to be more profitable than addition of extra axiomatic sequents. A program of formalization of mathematical ...

#### 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 ...

#### 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 Modified Subformula Property for the Modal Logic S4.2

(Wydawnictwo Uniwersytetu Łódzkiego, 2019)

The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is ...

#### Functional Completeness in CPL via Correspondence Analysis

(Wydawnictwo Uniwersytetu Łódzkiego, 2019)

Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only ...

#### The Method of Socratic Proofs Meets Correspondence Analysis

(Wydawnictwo Uniwersytetu Łódzkiego, 2019)

The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej ...

#### Minimal Sequent Calculi for Łukasiewicz’s Finitely-Valued Logics

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)

The primary objective of this paper, which is an addendum to the author’s [8], is to apply the general study of the latter to Łukasiewicz’s n-valued logics [4]. The paper provides an analytical expression of a 2(n−1)-place ...

#### A Useful Four-Valued Extension of the Temporal Logic KtT4

(Wydawnictwo Uniwersytetu Łódzkiego, 2018)

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 ...