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Boolean Valued Models, Boolean Valuations, and Löwenheim-Skolem Theorems
Boolean-valued models for first-order languages generalize two-valued models, in that the value range is allowed to be any complete Boolean algebra...
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Boolean-Like Algebras of Finite Dimension: From Boolean Products to Semiring Products
We continue the investigation, initiated in Salibra et al. (Found Sci, 2020), of Boolean-like algebras of dimension n (...
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Kripke-Completeness and Sequent Calculus for Quasi-Boolean Modal Logic
Quasi-Boolean modal algebras are quasi-Boolean algebras with a modal operator satisfying the interaction axiom. Sequential quasi-Boolean modal logics...
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Boolean Mereology
Most ordinary objects - cats, humans, mountains, ships, tables, etc. - have indeterminate mereological boundaries. If the theory of mereology is...
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Aristotelian and Boolean Properties of the Keynes-Johnson Octagon of Opposition
Around the turn of the 20th century, Keynes and Johnson extended the well-known square of opposition to an octagon of opposition, in order to account...
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Epistemic Monadic Boolean Algebras
Epistemic monadic Boolean algebras are obtained by enriching monadic Boolean algebras with a knowledge operator. Epistemic monadic logic as the...
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On Boolean Algebraic Structure of Proofs: Towards an Algebraic Semantics for the Logic of Proofs
We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in...
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The Boolean Many-Valued Solution to the Sorites Paradox
This paper offers the Boolean many-valued solution to the Sorites Paradox. According to the precisification-based Boolean many-valued theory, from...
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An event algebra for causal counterfactuals
“If the tower is any taller than 320 ms, it may collapse,” Eiffel thinks out loud. Although understanding this counterfactual poses no trouble, the...
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Kripke Contexts, Double Boolean Algebras with Operators and Corresponding Modal Systems
The notion of a context in formal concept analysis and that of an approximation space in rough set theory are unified in this study to define a...
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A Class of Implicative Expansions of Belnap-Dunn Logic in which Boolean Negation is Definable
Belnap and Dunn’s well-known 4-valued logic FDE is an interesting and useful non-classical logic. FDE is defined by using conjunction, disjunction...
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On the Representation of Boolean Magmas and Boolean Semilattices
A magma is an algebra with a binary operation \(\cdot \)...
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Grothendieck’s theory of schemes and the algebra–geometry duality
We shall address from a conceptual perspective the duality between algebra and geometry in the framework of the refoundation of algebraic geometry...
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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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Ernst Schröder on Algebra and Logic
This volume offers English translations of three early works by Ernst Schröder (1841-1902), a mathematician and logician whose philosophical...
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Basic Quasi-Boolean Expansions of Relevance Logics
The basic quasi-Boolean negation (QB-negation) expansions of relevance logics included in Anderson and Belnap’s relevance logic R are defined. We...
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Arithmetic is Necessary
(Goodsell, Journal of Philosophical Logic , 51 (1), 127-150 2022) establishes the noncontingency of sentences of first-order arithmetic, in a plausible...
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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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Contact Join-semilattices
Contact algebra is one of the main tools in region-based theory of space. In ([
7 ,8 ,22 ,23 ]) it is generalized by drop** the operation Boolean...