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Defining Formal Explanation in Classical Logic by Substructural Derivability
Precisely framing a formal notion of explanation is a hard problem of great relevance for several areas of scientific investigation such as computer...
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Peirce’s Dragon-Head Logic (R 501, 1901)
Peirce wrote in late 1901 a text on formal logic using a special Dragon-Head and Dragon-Tail notation in order to express the relation of logical...
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Classifying material implications over minimal logic
The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years, such as relevance logics,...
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Alternatives to CPL
In this chapter we focus on some non-classical logics which are weaker than CPL, like intuitionistic and intermediate (between intuitionistic and...
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Semilinear De Morgan monoids and epimorphisms
A representation theorem is proved for De Morgan monoids that are (i) semilinear , i.e., subdirect products of totally ordered algebras, and (ii) negati...
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Sequents and Trees An Introduction to the Theory and Applications of Propositional Sequent Calculi
This textbook offers a detailed introduction to the methodology and applications of sequent calculi in propositional logic. Unlike other texts...
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Complexity of Lambek Calculi with Modalities and of Total Derivability in Grammars
The Lambek calculus with the unit can be defined as the atomic theory (algebraic logic) of the class of residuated monoids. This calculus, being a...
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A Restricted Fragment of the Lambek Calculus with Iteration and Intersection Operations
The Lambek calculus (a variant of intuitionistic linear logic initially introduced for mathematical linguistics) enjoys natural interpretations over...
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Projectivity in (bounded) commutative integral residuated lattices
In this paper, we study projective algebras in varieties of (bounded) commutative integral residuated lattices. We make use of a well-established...
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Duality Results for (Co)Residuated Lattices
We present dualities (discrete duality, duality via truth and Stone duality) for implicative and (co)residuated lattices. In combination with our...
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Gluing Residuated Lattices
We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras,...
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Pointed Lattice Subreducts of Varieties of Residuated Lattices
We study the pointed lattice subreducts of varieties of residuated lattices (RLs) and commutative residuated lattices (CRLs), i.e. lattice subreducts...
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Unilinear residuated lattices: axiomatization, varieties and FEP
We characterize all residuated lattices that have height equal to 3 and show that the variety they generate has continuum-many subvarieties. More...
