Modal Reduction Principles across Relational Semantics
Sahlqvist theory is an important result in the model theory of modal logic, since it identifies a class of formulas which have effectively computable first order correspondents. Recently, this theory has been generalised to a larger set of logics by using their algebraic semantics. This fact has all...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad de Valladolid |
| Repositorio: | UVaDOC. Repositorio Documental de la Universidad de Valladolid |
| OAI Identifier: | oai:uvadoc.uva.es:10324/45558 |
| Acceso en línea: | http://uvadoc.uva.es/handle/10324/45558 |
| Access Level: | acceso abierto |
| Palabra clave: | Correspondence theory Sahlqvist theory Modal logic Many-valued modal logic Modal reduction principles Kripke models Polarity-based semantics Non-distributive logics Teoría de la correspondencia Teoría de Sahlqvist Lógica modal multi-valuada Modelos de Kripke 72 Filosofía |
| Sumario: | Sahlqvist theory is an important result in the model theory of modal logic, since it identifies a class of formulas which have effectively computable first order correspondents. Recently, this theory has been generalised to a larger set of logics by using their algebraic semantics. This fact has allowed researchers to define inequalities of formulas and to determine under which conditions these inequalities have effectively computable first order correspondents, that is, under which conditions they are Sahlqvist inequalities. Actually, there are algorithms that compute first order correspondents of these inequalities, such as ALBA algorithm. This algorithm translates any Sahlqvist inequality to a first order formula, but this translation still strongly depends on semantics. In this thesis, it is proposed a methodology to obtain first order correspondents of certain inequalities, called modal reduction principles, which are easily comparable across two relational semantics: crisp and many-valued polarity-based semantics. Concretely, this thesis presents an introduction to Sahlqvist theory and polarity-based semantics and proves that the first order correspondents of modal reduction principles are pure inclusion of binary relations on both semantics. |
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