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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 ...
Full Cut Elimination and Interpolation for Intuitionistic Logic with Existence Predicate
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)
In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that ...
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 ...
A Short and Readable Proof of Cut Elimination for Two First-Order Modal Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 2015)
A well established technique toward developing the proof theory of a Hilbert-style modal logic is to introduce a Gentzen-style equivalent (a Gentzenisation), then develop the proof theory of the latter, and finally transfer ...
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 ...
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 ...
Cut Elimination for Extended Sequent Calculi
(Wydawnictwo Uniwersytetu Łódzkiego, 2023-09-25)
We present a syntactical cut-elimination proof for an extended sequent calculus covering the classical modal logics in the \(\mathsf{K}\), \(\mathsf{D}\), \(\mathsf{T}\), \(\mathsf{K4}\), \(\mathsf{D4}\) and \(\mathsf{S4}\) ...