A Note on Absolutely Unorderable Combinatory Algebras

Authors: Lusin S.; Salibra A.

Source: Journal of Logic and Computation, Volume 13, Number 4, August 2003 , pp. 481-502(22)

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Abstract:

Plotkin has conjectured that there exists an absolutely unorderable combinatory algebra, namely a combinatory algebra which cannot be embedded in another combinatory algebra admitting a nontrivial compatible partial order. In this paper we prove that a wide class of combinatory algebras admits extensions with a nontrivial compatible partial order.

Document Type: Original article

Affiliations: 1: Dipartimento di Informatica, Università Ca'Foscari di Venezia, Via Torino 155, 30172 Venezia, Italy. , salibra@dsi.unive.it

Publication date: 2003-08-01

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The Journal of Logic and Computation aims to promote the growth of logic and computing, including, among others, the following areas of interest: Logical Systems, such as classical and non-classical logic, constructive logic, categorical logic, modal logic, type theory, feasible maths.... Logical issues in logic programming, knowledge-based systems and automated reasoning; logical issues in knowledge representation, such as non-monotonic reasoning and systems of knowledge and belief; logics and semantics of programming; specification and verification of programs and systems; applications of logic in hardware and VLSI, natural language, cincurrent computation, planning, and databases. The bulk of the content is technical scientific papers, although letters, reviews, and discussions, as well as relevant conference reviews, are included.