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Abstract
A propositional logic program P may be identified with a P f P f coalgebra on the set of atomic propositions in the program. The corresponding C(P f P f )coalgebra, where C(P f P f ) is the cofree comonad on P f P f , describes derivations by resolution. That correspondence has been developed to model firstorder programs in two ways, with lax semantics and saturated semantics, based on locally ordered categories and right Kan extensions respectively. We unify the two approaches, exhibiting them as complementary rather than competing, reflecting the theoremproving and proofsearch aspects of logic programming. While maintaining that unity, we further refine lax semantics to give finitary models of logic programs with existential variables, and to develop a precise semantic relationship between variables in logic programming and worlds in local state.
Original language  English 

Pages (fromto)  121 
Number of pages  21 
Journal  Journal of Logical and Algebraic Methods in Programming 
Volume  101 
Early online date  19 Jul 2018 
DOIs  
Publication status  Published  1 Dec 2018 
Keywords
 Logic programming, coalgebra, coinductive derivation tree, Lawvere theories, lax transformations, saturation
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Dive into the research topics of 'Logic programming: Laxness and saturation'. Together they form a unique fingerprint.Projects
 2 Finished


Coalgebraic Logic Programming for Type Inference
Power, J.
Engineering and Physical Sciences Research Council
1/09/13 → 31/01/17
Project: Research council