A Polynomial Model for Logics with a Prime Power Number of Truth Values

Hernando, A.; Roanes–Lozano, Eugenio; Laita, Luis M.

doi:10.1007/s10817-010-9191-0

Cited by 10 publications

(4 citation statements)

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“…As future work we will intend to work in two complementary research lines. On the one hand we intend to carry out the extension to many-valued logics and their applications [4,5,7] as well as to tackle the knowledge forgetting problem in modal logics [22]. If the underlying logic is many-valued, the algebraic varieties of the polynomial translations of the propositions do not behave intuitively (see [1]).…”

Section: Discussionmentioning

confidence: 99%

“…[1] for an introduction). This relationship also provides mathematical foundations for a number of Knowledge Representation and Reasoning (KRR) methods and algorithms, encompassing applications since the pioneer works for classical bivalued logic [2,3] to extensions for multivalued logics [4,5,6,7]. The framework has also been extended to other logics for Artificial Intelligence (AI) as the paraconsistent logic [8], and even towards other nonstandard reasoning tasks as the argument-based one (cf.…”

Section: Introductionmentioning

confidence: 99%

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A logic-algebraic tool for reasoning with Knowledge-Based Systems

Alonso-Jiménez¹,

Aranda-Corral²,

Borrego-Díaz³

et al. 2018

Journal of Logical and Algebraic Methods in Programming

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A detailed exposition of foundations of a logic-algebraic model for reasoning with knowledge bases specified by propositional (Boolean) logic is presented. The model is conceived from the logical translation of usual derivatives on polynomials (on residue rings) which is used to design a new inference rule of algebro-geometric inspiration. Soundness and (refutational) completeness of the rule are proved. Some applications of the tools introduced in the paper are shown.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A logic-algebraic tool for reasoning with Knowledge-Based Systems

Alonso-Jiménez¹,

Aranda-Corral²,

Borrego-Díaz³

et al. 2018

Journal of Logical and Algebraic Methods in Programming

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show abstract

“…In case the number of truth values of the logic is a power of a prime number, the model can be also adapted [27].…”

Section: Introductionmentioning

confidence: 99%

The Logics’ Explorer: a Maple package for exploring finite many-valued propositional logics

Roanes–Lozano

Alonso

Hernando

et al. 2011

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The big computer algebra systems like Maple are no longer restricted to symbolic computations, but are becoming general purpose tools for engineers, mathematicians, and scientists instead. We have worked for a long time with many-valued logics and we believe that a flexible and comfortable tool that allowed to perform logical computations (for instance, to explore properties) in any existing or proposed many-valued logic with any notation for the truth values of the logic, could be very useful and time-saving. Therefore we have implemented such an extension of Maple that goes beyond Maple's logic package and also beyond some previous implementations of these authors included with the Derive and Macsyma distributions some years ago. The logical connectives can be defined both using truth tables or in a functional way.

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“…Se define un modelo [21] que combina los dos descritos anteriormente. Este modelo utiliza varios resultados matemáticos [20,22,39] que permiten resolver problemas relacionados con lógica proposicional mediante técnicas algebraicas.…”

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Modelo algebraico con precálculo de operaciones para la detección de situaciones peligrosas en grandes instalaciones ferroviarias

Martínez¹

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The safety of a railway station is a very important issue considered very labour-intensive. Different authors have developed different approaches in order to detect automatically the safety of small to midsize railway stations. Although these approaches are very simple to implement, they have the drawback of being unsuitable to large stations, since the algorithm takes large time to be run.The present PhD thesis has the objective of presenting a new logicalgebraic model able to: I) check the safety in large railway stations when trains are located in a one or more sections, and II) precalculate different states of the station (trains located in sections, colour of the semaphores, position of the switches, etc ...). Once a precalculation is made for certain state, the time to check the safety in large railway networks is reduced dramatically. As a case study we provide a comparision between several models in a real large railway station (Chamartín) showing that the time results are suitable to check the safety of such a station.

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A Polynomial Model for Logics with a Prime Power Number of Truth Values

Cited by 10 publications

References 19 publications

A logic-algebraic tool for reasoning with Knowledge-Based Systems

A logic-algebraic tool for reasoning with Knowledge-Based Systems

The Logics’ Explorer: a Maple package for exploring finite many-valued propositional logics

Modelo algebraico con precálculo de operaciones para la detección de situaciones peligrosas en grandes instalaciones ferroviarias

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