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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, ...
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 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 ...
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 ...