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Infinitary first-order categorical logic

We present a unified categorical treatment of completeness theorems for several classical and intuitionistic infinitary logics with a proposed axiomatization. This provides new completeness theorems and subsumes previous ones by God...

Applied mathematics

  • 2019
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  • Jimp
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Result

A new hierarchy of infinitary logics in abstract algebraic logic

In this article we investigate infinitary propositional logics from the perspective of their completeness properties in abstract algebraic logic. It is well-known that every finitary logic is complete with respect ...

Pure mathematics

  • 2017
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  • Jimp
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Result

On Strong Standard Completeness in Some MTL-Delta Expansions

In this paper, inspired by the previous work of Franco Montagna on infinitary with infinitary rules) which is strongly complete with respect to the standard algebra [0,1]*. This system will be an expansion of Monoidal t-norm-based <...

Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

  • 2017
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  • Jimp
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Result

Extension Properties and Subdirect Representation in Abstract Algebraic Logic

Log 105(3): 521–551, 2017), of infinitary propositional logics from algebraic logic. If follows from the Lindenbaum Lemma used in standard proofs of algebraic completeness that, in every finitary logic, (completel...

Pure mathematics

  • 2018
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  • Jimp
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Result

Lindenbaum and Pair Extension Lemma in Infinitary Logics

The abstract Lindenbaum lemma is a crucial result in algebraic logic saying given logic. Its usual formulation is however limited to finitary logics, i.e., logics with Hilbert-style axiomatization using finitary ru...

Pure mathematics

  • 2018
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  • D
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  • Link
Result

An approach to stochastic processes via non-classical logic

Within the infinitary variety of sigma-complete Riesz MV-algebras RMV sigma, we introduce the algebraic analogue of a random variable as a homomorphism defined it to define stochastic processes in the framework of non-classical logic

Pure mathematics

  • 2021
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  • Jimp
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Result

A Note on Axiomatizations of Pavelka-style Complete Fuzzy Logics

and truth, was previously studied mainly in the context of logics with continuous connectives. It is known that in some other logics one can use infinitary deduction rule(s of this idea for fuzzy logics which expa...

Pure mathematics

  • 2016
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  • Jimp
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  • Link
Result

A 0-1 Law in Mathematical Fuzzy Logic

This paper continues the theoretical study of weighted structures in mathematical fuzzy logic focusing on the finite model theory of fuzzy logics valued on arbitrary finite MTL-chains. We show that for any first-order (or infini...

Pure mathematics

  • 2022
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  • Jimp
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Result

Infinitary generalizations of Deligne's completeness theorem

is essentially a completeness theorem for a certain infinitary logic that we call kappa, Karp's completeness theorem for infinitary classical logic....

Pure mathematics

  • 2020
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  • Jimp
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  • Link
Result

On clones of infinitary algebras and their initial segments

We give the respective answers to the question of when the existence of all local clone isomorphisms implies the existence of a global clone isomorphism for term clones, polynomial clones and centralizer clones of universal algebras of an infinit...

BA - Obecná matematika

  • 2010
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  • Jx
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