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Prelogical relations

HONSELL, Furio
•
SANNELLA, D.
2002
  • journal article

Periodico
INFORMATION AND COMPUTATION
Abstract
We study a weakening of the notion of logical relations, called prelogical relations, that has many of the features that make logical relations so useful as well as further algebraic properties including composability. The basic idea is simply to require the reverse implication in the definition of logical relations to hold only for pairs of functions that are expressible by the same lambda term. Prelogical relations are the minimal weakening of logical relations that gives composability for extensional structures and simultaneously the most liberal definition that gives the Basic Lemma. Prelogical predicates (i.e., unary prelogical relations) coincide with sets that are invariant under Kripke logical relations with varying arity as introduced by Jung and Tiuryn, and prelogical relations are the closure under projection and intersection of logical relations. These conceptually independent characterizations of prelogical relations suggest that the concept is rather intrinsic and robust. The use of prelogical relations gives an improved version of Mitchell's representation independence theorem which characterizes observational equivalence for all signatures rather than just for first-order signatures. Prelogical relations can be used in place of logical relations to give an account of data refinement where the fact that prelogical relations compose explains why stepwise refinement is sound.
DOI
10.1006/inco.2002.3115
WOS
WOS:000178847400003
Archivio
http://hdl.handle.net/11390/714049
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-0037057839
http://www.sciencedirect.com/science/article/pii/S0890540102931159
Diritti
closed access
Soggetti
  • Data refinement

  • Logical relation

  • Representation indepe...

  • Semantic

  • Typed lambda calculus...

Scopus© citazioni
5
Data di acquisizione
Jun 7, 2022
Vedi dettagli
Web of Science© citazioni
6
Data di acquisizione
Feb 6, 2024
Visualizzazioni
3
Data di acquisizione
Apr 19, 2024
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