Bulletin of the Section of Logic: Ostatnio dodane
Wyświetlanie pozycji 121-140 z 224
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Empirical Negation, Co-Negation and the Contraposition Rule II: Proof-Theoretical Investigations
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)We continue the investigation of the first paper where we studied logics with various negations including empirical negation and co-negation. We established how such logics can be treated uniformly with R. Sylvan's CCω as ... -
From Intuitionism to Brouwer's Modal Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication ... -
The Phenomenology of Second-Level Inference: Perfumes in The Deductive Garden
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-12-30)We comment on certain features that second-level inference rules commonly used in mathematical proof sometimes have, sometimes lack: suppositions, indirectness, goal-simplification, goal-preservation and premise-preservation. ... -
Equality Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-11-04)In this paper, we introduce and study a corresponding logic to equality-algebras and obtain some basic properties of this logic. We prove the soundness and completeness of this logic based on equality-algebras and local ... -
Module Structure on Effect Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-11-04)In this paper, by considering the notions of effect algebra and product effect algebra, we define the concept of effect module. Then we investigate some properties of effect modules, and we present some examples on them. ... -
New Modification of the Subformula Property for a Modal Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-11-04)A modified subformula property for the modal logic KD with the additionalaxiom □ ◊(A ∨ B) ⊃ □ ◊ A ∨ □ ◊B is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a ... -
Empirical Negation, Co-negation and Contraposition Rule I: Semantical Investigations
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-11-04)We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then ... -
Proof Compression and NP Versus PSPACE II
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-11-04)We upgrade [3] to a complete proof of the conjecture NP = PSPACE that is known as one of the fundamental open problems in the mathematical theory of computational complexity; this proof is based on [2]. Since minimal ... -
A Topological Approach to Tense LMn×m-Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-03-30)In 2015, tense n × m-valued Lukasiewicz–Moisil algebras (or tense LMn×m-algebras) were introduced by A. V. Figallo and G. Pelaitay as an generalization of tense n-valued Łukasiewicz–Moisil algebras. In this paper we continue ... -
May the Sea-Battle Tommorow Not Happen?
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-03-30)This note provides a review of the book 'On the Sea-Battle Tomorrow That May Not Happen' by Tomasz Jarmużek. -
The Dynamic Epistemic Logic for Actual Knowledge
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-03-30)The dynamic epistemic logic for actual knowledge models the phenomenon of actual knowledge change when new information is received. In contrast to the systems of dynamic epistemic logic which have been discussed in the ... -
Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-03-30)Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are ... -
Nilpotent Minimum Logic NM and Pretabularity
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-03-30)This paper deals with pretabularity of fuzzy logics. For this, we first introduce two systems NMnfp and NM½, which are expansions of the fuzzy system NM (Nilpotent minimum logic), and examine the relationships between NMnfp ... -
Disjunctive Multiple-Conclusion Consequence Relations
(Wydawnictwo Uniwersytetu Łódzkiego, 2019-12-31)The concept of multiple-conclusion consequence relation from [8] and [7] is considered. The closure operation C assigning to any binary relation r (dened on the power set of a set of all formulas of a given language) the ... -
Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2019-12-31)Sentences containing definite descriptions, expressions of the form `The F', can be formalised using a binary quantier that forms a formula out of two predicates, where ℩x[F;G] is read as `The F is G'. This is an innovation ... -
An Investigation into Intuitionistic Logic with Identity
(Wydawnictwo Uniwersytetu Łódzkiego, 2019-12-31)We define Kripke semantics for propositional intuitionistic logic with Suszko’s identity (ISCI). We propose sequent calculus for ISCI along with cut-elimination theorem. We sketch a constructive interpretation of Suszko’s ... -
Many Faces of Lattice Tolerances
(Wydawnictwo Uniwersytetu Łódzkiego, 2019-12-31)Our aim is to overview and discuss some of the most popular approaches to the notion of a tolerance relation in algebraic structures with the special emphasis on lattices. -
Semantical Proof of Subformula Property for the Modal Logics K4.3, KD4.3, and S4.3
(Wydawnictwo Uniwersytetu Łódzkiego, 2019-12-31)The main purpose of this paper is to give alternative proofs of syntactical and semantical properties, i.e. the subformula property and the nite model property, of the sequent calculi for the modal logics K4.3, KD4.3, and ... -
Modal Boolean Connexive Logics: Semantics and Tableau Approach
(Wydawnictwo Uniwersytetu Łódzkiego, 2019-10-30)In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. ... -
A Note on Distributive Triples
(Wydawnictwo Uniwersytetu Łódzkiego, 2019-10-30)Even if a lattice L is not distributive, it is still possible that for particular elements x, y, z ∈ L it holds (x∨y) ∧z = (x∧z) ∨ (y ∧z). If this is the case, we say that the triple (x, y, z) is distributive. In this note ...