Bulletin of the Section of Logic: Recent submissions
Now showing items 101-120 of 230
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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 ... -
On Complete Representations and Minimal Completions in Algebraic Logic, Both Positive and Negative Results
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-07-21)Fix a finite ordinal \(n\geq 3\) and let \(\alpha\) be an arbitrary ordinal. Let \(\mathsf{CA}_n\) denote the class of cylindric algebras of dimension \(n\) and \(\sf RA\) denote the class of relation algebras. Let ... -
A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-11-09)In this paper, we shall show that the following translation \(I^M\) from the propositional fragment \(\bf L_1\) of Leśniewski's ontology to modal logic \(\bf KTB\) is sound: for any formula \(\phi\) and \(\psi\) of \(\bf ... -
The (Greatest) Fragment of Classical Logic that Respects the Variable-Sharing Principle (in the FMLA-FMLA Framework)
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-05-27)We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, ... -
On the Category of EQ-algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-01-20)In this paper, we studied the category of EQ-algebras and showed that it is complete, but it is not cocomplete, in general. We proved that multiplicatively relative EQ-algebras have coequlizers and we calculated coproduct ... -
Neighbourhood Semantics for Graded Modal Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-07-14)We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We ... -
A General Model of Neutrosophic Ideals in BCK/BCI-algebras Based on Neutrosophic Points
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-08-15)More general form of (∈, ∈ ∨q)-neutrosophic ideal is introduced, and their properties are investigated. Relations between (∈, ∈)-neutrosophic ideal and (∈, ∈ ∨q(kT ,kI ,kF ))-neutrosophic ideal are discussed. Characterizations ... -
Falling Shadow Theory with Applications in Hoops
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-01-20)The falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between ... -
Tense Operators on BL-algebras and Their Applications
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-05-28)In this paper, the notions of tense operators and tense filters in \(BL\)-algebras are introduced and several characterizations of them are obtained. Also, the relation among tense \(BL\)-algebras, tense \(MV\)-algebras ... -
A Note on Gödel-Dummet Logic LC
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-07-01)Let \(A_{0},A_{1},...,A_{n}\) be (possibly) distintict wffs, \(n\) being an odd number equal to or greater than 1. Intuitionistic Propositional Logic IPC plus the axiom \((A_{0}\rightarrow A_{1})\vee ...\vee (A_{n-1}\rightarrow ... -
A Note on 3×3-valued Łukasiewicz Algebras with Negation
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-05-27)In 2004, C. Sanza, with the purpose of legitimizing the study of \(n\times m\)-valued Łukasiewicz algebras with negation (or \(\mathbf{NS}_{n\times m}\)-algebras) introduced \(3 \times 3\)-valued Łukasiewicz algebras with ... -
Omitting Types in Fragments and Extensions of First Order Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-05-28)Fix \(2 < n < \omega\). Let \(L_n\) denote first order logic restricted to the first n variables. Using the machinery of algebraic logic, positive and negative results on omitting types are obtained for \(L_n\) and for ... -
Extended MR with Nesting of Predicate Expressions as a Basic Logic for Social Phenomena
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-06-30)In this article, we present the positional logic that is suitable for the formalization of reasoning about social phenomena. It is the effect of extending the Minimal Realisation (MR) logic with new expressions. These ... -
Common Knowledge, Common Attitudes and Social Reasoning
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-06-30)For as long as there have been theories about common knowledge, they have been exposed to a certain amount of skepticism. Recent more sophisticated arguments question whether agents can acquire common attitudes and whether ... -
Tableau Systems for Epistemic Positional Logics
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-06-30)The goal of the article is twofold. The first one is to provide logics based on positional semantics which will be suitable for the analysis of epistemic modalities such as ‘agent ... knows/beliefs that ...’. The second ... -
The Good, the Bad and the Right: Formal Reductions among Deontic Concepts
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-06-30)The present article provides a taxonomic analysis of bimodal logics of normative ideality and normative awfulness, two notions whose meaning is here explained in terms of the moral values pursued by a given community. ... -
Towards a Logic of Value and Disagreement via Imprecise Measures
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-06-30)After putting forward a formal account of value disagreement via imprecise measures, I develop a logic of value attribution and of (dis)agreement based on (exact) truthmaker semantics. -
Reasoning about Social Phenomena
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-06-30) -
What Is the Sense in Logic and Philosophy of Language
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-06-30)In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception ... -
Compounding Objects
(Wydawnictwo Uniwersytetu Łódzkiego, 2020-06-30)We prove a characterization theorem for filters, proper filters and ultrafilters which is a kind of converse of Łoś's theorem. It is more natural than the usual intuition of these terms as large sets of coordinates, which ...