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Title: A generalisation of pre-logical predicates and its applications
Author: Katsumata, Shin-ya
ISNI:       0000 0004 2725 0501
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2005
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This thesis proposes a generalisation of pre-logical predicates to simply typed formal systems and their categorical models. We analyse the three elements involved in pre-logical predicates -- syntax, semantics and predicates -- within a categorical framework for typed binding syntax and semantics. We then formulate generalised pre-logical predicates and show two distinguishing properties: a) equivalence with the basic lemma and b) closure of binary pre-logical relations under relational composition. To test the adequacy of this generalisation, we derive pre-logical predicates for various calculi and their categorical models including variations of lambda calculi and non-lambda calculi such as many-sorted algebras as well as first-order logic. We then apply generalised pre-logical predicates to characterising behavioural equivalence. Examples of constructive data refinement of typed formal systems are shown, where behavioural equivalence plays a crucial role in achieving data abstraction.
Supervisor: Sannella, Donald. ; Stark, Ian. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Computer Science ; Observational Equivalence ; Logical Relation