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    • A 2 Set-Up Binary Routley Semantics for Gödelian 3-Valued Logic G3 and Its Paraconsistent Counterpart G3\(_\text{Ł}^\leq\) 

      Robles, Gemma; Méndez, José M. (Wydawnictwo Uniwersytetu Łódzkiego, 2022-10-14)
      G3 is Gödelian 3-valued logic, G3\(_\text{Ł}^\leq\) is its paraconsistent counterpart and G3\(_\text{Ł}^1\) is a strong extension of G3\(_\text{Ł}^\leq\). The aim of this paper is to endow each one of the logics just ...

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

      Robles, Gemma; López, Sandra M.; Blanco, José M.; Recio, Marcos M.; Paradela, Jesús R. (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 

      Łazarz, Marcin; Siemieńczuk, Krzysztof (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 

      Gao, Feng; Tourlakis, George (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 

      Gyenis, Zalán (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 

      Ilić, Mirjana (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 

      Ferreira, Fernando; Ferreira, Gilda (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 

      French, Rohan; Humberstone, Lloyd (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 

      Braüner, Torben (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 

      Grygiel, Joanna (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 

      Hao, Yunge; Tourlakis, George (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 

      Takano, Mitio (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 

      Assaye, Berhanu; Alemneh, Mihret; Tefera, Gerima (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 ...

    • Basic Four-Valued Systems of Cyclic Negations 

      Grigoriev, Oleg; Zaitsev, Dmitry (Wydawnictwo Uniwersytetu Łódzkiego, 2022-10-25)
      We consider an example of four valued semantics partially inspired by quantum computations and negation-like operations occurred therein. In particular we consider a representation of so called square root of negation ...

    • Bayesian Propositional Logic 

      Jarmużek, Tomasz; Klonowski, Mateusz; Malinowski, Jacek (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 

      Khan, Faiz Muhammad; Khan, Imran; Ahmad, Waqas (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 ...

    • Bilateral Rules as Complex Rules 

      Ceragioli, Leonardo (Wydawnictwo Uniwersytetu Łódzkiego, 2023-07-18)
      Proof-theoretic semantics is an inferentialist theory of meaning originally developed in a unilateral framework. Its extension to bilateral systems opens both opportunities and problems. The problems are caused especially ...

    • A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation 

      Kurbis, Nils (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 

      Błaszczyk, Piotr; Fila, Marlena (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 ...

    • The Cardinal Squaring Principle and an Alternative Axiomatization of NFU 

      Adlešić, Tin; Čačić, Vedran (Wydawnictwo Uniwersytetu Łódzkiego, 2023-09-28)
      In this paper, we rigorously prove the existence of type-level ordered pairs in Quine’s New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU + Inf + AC). The proof uses the cardinal ...