Now showing items 1-20 of 152

• #### 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. ...
• #### A Note on some Characterization of Distributive Lattices of Finite Length ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)
Using known facts we give a simple characterization of the distributivity of lattices of finite length.
• #### 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 ...
• #### Algebraic Characterization of the Local Craig Interpolation Property ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2018)
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. ...
• #### 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 ...
• #### An Elementary Proof of Strong Normalization for Atomic F ﻿

(Uniwersytet Łódzki. Katedra Logiki i Metodologii Nauk, 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 F_{at} (a predicative restriction of Girard’s system F).
• #### An Observation Concerning Porte’s Rule in Modal Logic ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)
It is well known that no consistent normal modal logic contains (as theorems) both ◊A and ◊¬A (for any formula A). Here we observe that this claim can be strengthened to the following: for any formula A, either no consistent ...
• #### Analytic Non-Labelled Proof-Systems for Hybrid Logic: Overview and a couple of striking facts ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2022-01-07)
This paper is about non-labelled proof-systems for hybrid logic, that is, proofsystems where arbitrary formulas can occur, not just satisfaction statements. We give an overview of such proof-systems, focusing on analytic ...
• #### Applications of Algebra in Logic and Computer Science – the Past and the Future ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2018)
We present the history of the conference Applications of Algebra in Logic and Computer Science, whose twenty-third edition will be held in March, 2019. At the end we outline some plans for the future.
• #### An Arithmetically Complete Predicate Modal Logic ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2021-08-23)
This paper investigates a first-order extension of GL called $$\textup{ML}^3$$. We outline briefly the history that led to $$\textup{ML}^3$$, its key properties and some of its toolbox: the \emph{conservation theorem}, its ...
• #### 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.
• #### B-almost distributive fuzzy lattice ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2018)
The paper introduces the concept of B-Almost distributive fuzzy lattice (BADFL) in terms of its principal ideal fuzzy lattice. Necessary and sufficient conditions for an ADFL to become a B-ADFL are investigated. We also ...
• #### Bayesian Propositional Logic ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2017)
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 ...
• #### A Benchmark Similarity Measures for Fermatean Fuzzy Sets ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2022-06-08)
In this paper, we utilized triangular conorms (S-norm). The essence of using S-norm is that the similarity order does not change using different norms. In fact, we are investigating for a new conception for calculating the ...
• #### A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2019)
This paper presents a way of formalising definite descriptions with a binary quantifier ℩, where ℩x[F, G] is read as `The F is G'. Introduction and elimination rules for ℩ in a system of intuitionist negative free logic ...
• #### Cantor on Infinitesimals. Historical and Modern Perspective ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2020-06-30)
In his 1887's Mitteilungen zur Lehre von Transfiniten, Cantor seeks to prove inconsistency of infinitesimals. We provide a detailed analysis of his argument from both historical and mathematical perspective. We show that ...
• #### Categorical Abstract Algebraic Logic: Referential π-Institutions ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2015)
Wójcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of ...
• #### Categorical Abstract Algebraic Logic: Pseudo-Referential Matrix System Semantics ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2018)
This work adapts techniques and results first developed by Malinowski and by Marek in the context of referential semantics of sentential logics to the context of logics formalized as π-institutions. More precisely, the ...
• #### 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 ...
• #### Categorical Dualities for Some Two Categories of Lattices: An Extended Abstract ﻿

(Wydawnictwo Uniwersytetu Łódzkiego, 2022-08-02)
The categorical dualities presented are: (first) for the category of bi-algebraic lattices that belong to the variety generated by the smallest non-modular lattice with complete (0,1)-lattice homomorphisms as morphisms, ...