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Canonical Relativized Cylindric Set Algebras and Weak Associativity
Canonical relativized cylindric set algebras are used to sharpen the relative representation theorem for weakly associative relation algebras, that...
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A Categorical Equivalence for Tense Nelson Algebras
In this paper we present a category equivalent to that of tense Nelson algebras. The objects in this new category are pairs consisting of an...
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Undecidability of Algebras of Binary Relations
Let S be a signature of operations and relations definable in relation algebra (e.g. converse, composition, containment, union, identity, etc.), let...
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Freeing Structural Realism from Model Theory
Structural realists contend that the properties and relations in the world are more fundamental than the individuals. However, the standard model...
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Blow Up and Blur Constructions in Algebraic Logic
Fix \(2<n> <\omega \) and let \(\mathsf{CA}_n\)...
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Hereditarily Structurally Complete Intermediate Logics: Citkin’s Theorem Via Duality
A deductive system is said to be structurally complete if its admissible rules are derivable. In addition, it is called hereditarily structurally...
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A Cook’s Tour of Duality in Logic: From Quantifiers, Through Vietoris, to Measures
We identify and highlight certain landmark results in Samson Abramsky’s work which we believe are fundamental to current developments and future...
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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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Conclusions and Open Problems
The present book aims at providing readers with a primer on logics of variable inclusion, systems that have attracted more and more attention in the...
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The Four Essential Aristotelian Syllogisms, via Substitution and Symmetry
There being no limit to the number of categories, there is no limit to the number of Aristotelian syllogisms. Aristotle showed that this potential...
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Modal Logics that Bound the Circumference of Transitive Frames
For each natural number n we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater...
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Algebraic Semantics for Hybrid Logics
We introduce hybrid algebras as algebraic semantics for hybrid languages with nominals and, possibly, the satisfaction operator. We establish a...
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A Scientific Autobiography
This is a short autobiography consisting of personal recollections and experiences in my academic life. It starts from my student days, and covers...
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Compositionality in Context
Compositionality is a principle used in logic, philosophy, mathematics, linguistics, and computer science for assigning meanings to language...
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Abstract Algebraic Logic
This chapter is a brief introduction to abstract algebraic logic. It is organized around the central notion of algebraizability, with particular...
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First-Order Predicate Logics
The last chapter gives a short introduction to the study of first-order predicate logics built over weakly implicative logics. We follow a...
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A Simple Logic of Functional Dependence
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence...
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Reconciling First-Order Logic to Algebra
We start from the algebraic method of theorem-proving based on the translation of logic formulas into polynomials over finite fields, and adapt the...
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Introducing Boolean Semilattices
We present and discuss a variety of Boolean algebras with operators that is closely related to the variety generated by all complex algebras of...