Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.634948
Title: Minimal model reasoning for modal logic
Author: Papacchini, Fabio
ISNI:       0000 0004 5353 3898
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2015
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Abstract:
Model generation and minimal model generation are useful for tasks such as model checking, query answering and for debugging of logical specifications. Due to this variety of applications, several minimality criteria and model generation methods for classical logics have been studied. Minimal model generation for modal logics how ever did not receive the same attention from the research community. This thesis aims to fill this gap by investigating minimality criteria and designing minimal model generation procedures for all the sublogics of the multi-modal logic S5(m) and their extensions with universal modalities. All the procedures are minimal model sound and complete, in the sense that they generate all and only minimal models. The starting point of the investigation is the definition of a Herbrand semantics for modal logics on which a syntactic minimality criterion is devised. The syntactic nature of the minimality criterion allows for an efficient minimal model generation procedure, but, on the other hand, the resulting minimal models can be redundant or semantically non minimal with respect to each other. To overcome the syntactic limitations of the first minimality criterion, the thesis moves from minimal modal Herbrand models to semantic minimality criteria based on subset-simulation. At first, theoretical procedures for the generation of models minimal modulo subset-simulation are presented. These procedures for the generation of models minimal modulo subset-simulation are minimal model sound and complete, but they might not terminate. The minimality criterion and the procedures are then refined in such a way that termination can be ensured while preserving minimal model soundness and completeness.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.634948  DOI: Not available
Keywords: Minimal Model Reasoning ; Tableaux Methods ; Modal Logic ; Model Generation ; Minimal Model Generation ; Subset-simulation ; Automated Reasoning
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