### Recent Submissions

• #### 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 ...