Equivalences, Identities, Symmetric Differences, and Congruences in Orthomodular Lattices
, 2003 It is shown that operations of equivalence cannot serve for building algebras which would induce orthomodular lattices as the operations of implication can. Several properties of equivalence operations have been investigated.
Megill, Norman D., Pavicic, Mladen
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Łukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems [PDF]
, 2010 A novel approach to self-organizing, highly-complex systems (HCS), such as living organisms and artificial intelligent systems (AIs), is presented which is relevant to Cognition, Medical Bioinformatics and Computational Neuroscience.
Baianu, Professor I.C. +2 more
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Notes on divisible MV-algebras
, 2016 In these notes we study the class of divisible MV-algebras inside the algebraic hierarchy of MV-algebras with product. We connect divisible MV-algebras with $\mathbb Q$-vector lattices, we present the divisible hull as a categorical adjunction and we ...
Lapenta, Serafina, Leustean, Ioana
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Nonlinear Models of Neural and Genetic Network Dynamics:\ud \ud Natural Transformations of Łukasiewicz Logic LM-Algebras in a Łukasiewicz-Topos as Representations of Neural Network Development and Neoplastic Transformations \ud [PDF]
, 2011 A categorical and Łukasiewicz-Topos framework for Algebraic Logic models of nonlinear dynamics in complex functional systems such as Neural Networks, Cell Genome and Interactome Networks is introduced.
Baianu, Professor I.C.
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Classical Control, Quantum Circuits and Linear Logic in Enriched Category Theory
, 2020 We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for
Rennela, Mathys, Staton, Sam
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Coherence in Modal Logic [PDF]
, 2018 A variety is said to be coherent if the finitely generated subalgebras of its finitely presented members are also finitely presented. In a recent paper by the authors it was shown that coherence forms a key ingredient of the uniform deductive ...
Kowalski, Tomasz, Metcalfe, George
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Canonical extensions and ultraproducts of polarities
, 2018 J{\'o}nsson and Tarski's notion of the perfect extension of a Boolean algebra with operators has evolved into an extensive theory of canonical extensions of lattice-based algebras. After reviewing this evolution we make two contributions.
Goldblatt, Robert
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Interval valued $(\in,\ivq)$-fuzzy filters of pseudo $BL$-algebras
, 2008 We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued $(\in,\ivq)$-fuzzy filters of pseudo $BL$-algebras and investigate some of ...
A Di Nola +37 more
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Algebra and logic. Some problems [PDF]
, 2013 The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness.
Plotkin, Boris
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Semantics out of context: nominal absolute denotations for first-order logic and computation
, 2016 Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation.
Gabbay, Murdoch J.
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