2 research outputs found
Sound search in a denotational semantics for first order logic
In this paper we adapt the definitions and results from Apt and Vermeulen on
`First order logic as a constraint programming language' (in: Proceedings of
LPAR2001, Baaz and Voronkov (eds.), Springer LNAI 2514) to include important
ideas about search and choice into the system. We give motivating examples.
Then we set up denotational semantics for first order logic as follows: the
semantic universe includes states that consist of two components: a
substitution, which can be seen as the computed answer; and a constraint
satisfaction problem, which can be seen as the residue of the original problem,
yet to be handled by constraint programming. The interaction between these
components is regulated by an operator called: infer. In this paper we regard
infer as an operator on sets of states to enable us to analyze ideas about
search among states and choice between states.
The precise adaptations of definitions and results are able to deal with the
examples and we show that, given several reasonable conditions, the new
definitions ensure soundness of the system with respect to the standard
interpretation of first order logic. In this way the `reasonable conditions'
can be read as conditions for sound search.
We indicate briefly how to investigate efficiency of search in future
research.Comment: To appear in print shortly in the Progress in Computer Science Series
of Novapublication