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Representability of Kleene Posets and Kleene Lattices
A Kleene lattice is a distributive lattice equipped with an antitone involution and satisfying the so-called normality condition. These lattices were...
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Relating Kleene Algebras with Pseudo Uninorms
This paper explores a strict relation between two core notions of the semantics of programs and of fuzzy logics: Kleene Algebras and (pseudo)...
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Strong Kleene Metainferential Logics
In this chapter, we will introduce the most studied family of pure and impure mixed metainferential logics of level 1: the Strong Kleene...
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Popper’s Correspondence with Stephen Cole Kleene
Stephen Cole Kleene (1909–1994) was an American logician, well-known for his fundamental work in various fields of theoretical computer science, such...
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Embedding Kozen-Tiuryn Logic into Residuated One-Sorted Kleene Algebra with Tests
Kozen and Tiuryn have introduced the substructural logic \(\textsf{S}\)...
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How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy
Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies...
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Tense Operators on Distributive Lattices with Implication
Inspired by the definition of tense operators on distributive lattices presented by Chajda and Paseka in 2015, in this paper, we introduce and study...
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Implication in Sharply Paraorthomodular and Relatively Paraorthomodular Posets
In this paper we show that several classes of partially ordered structures having paraorthomodular reducts, or whose sections may be regarded as...
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Proof Theory of Paraconsistent Weak Kleene Logic
Paraconsistent Weak Kleene Logic (PWK) is the 3-valued propositional logic defined on the weak Kleene tables and with two designated values. Most of...
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A Logical Modeling of Severe Ignorance
In the logical context, ignorance is traditionally defined recurring to epistemic logic. In particular, ignorance is essentially interpreted as “lack...
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A Few Historical Glimpses into the Interplay Between Algebra and Logic and Investigations into Gautama Algebras
This chapter consists of two parts. PART I presents a few historical glimpses into the fascinating interplay between algebra and logic that...
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A Few Historical Glimpses into the Interplay Between Algebra and Logic and Investigations into Gautama Algebras
This chapter consists of two parts. PART I presents a few historical glimpses into the fascinating interplay between algebra and logic that...
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Recognizability in Residuated Lattices
The objective of this work is to show that modules over a fixed residuated lattice...
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PBZ \(^{*}\) –Lattices: Ordinal and Horizontal Sums
PBZ \(^{*}\) –lattices are lattices with additional operations that arise in the context of the unsharp approach to quantum logic. They include...
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Ockham Algebras—An Urquhart Legacy
We highlight the fundamental influence that the work of Alasdair Urquhart has had in the area of distributive lattice-ordered algebras and in...
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Approximating Approximate Reasoning: Fuzzy Sets and the Ershov Hierarchy
Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies...
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Probability and Symmetric Logic
In this paper we study the interaction between symmetric logic and probability. In particular, we axiomatize the convex hull of the set of...
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Simple Systems and Complex Systems
In relational system theory, the difference between a simple system and a complex system is that a simple system is predicative while a complex...
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