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Abstract
Every variablefree logic program induces a P_{f} P _{f} coalgebra on the set of atomic formulae in the program. The coalgebra p sends an atomic formula A to the set of the sets of atomic formulae in the antecedent of each clause for which A is the head. In an earlier paper, we identified a variablefree logic program with a P_{f} P _{f} coalgebra on Set and showed that, if C(P_{f} P _{f} ) is the cofree comonad on P_{f} P _{f} , then given a logic program P qua P_{f} P _{f} coalgebra, the corresponding C(P_{f} P _{f} )coalgebra structure describes the parallel andor derivation trees of P. In this paper, we extend that analysis to arbitrary logic programs. That requires a subtle analysis of lax natural transformations between Posetvalued functors on a Lawvere theory, of locally ordered endofunctors and comonads on locally ordered categories, and of coalgebras, oplax maps of coalgebras, and the relationships between such for locally ordered endofunctors and the cofree comonads on them.
Original language  English 

Title of host publication  Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 
Pages  268282 
Number of pages  15 
Volume  6859 LNCS 
DOIs  
Publication status  Published  2011 
Event  4th International Conference on Algebra and Coalgebra in Computer Science, CALCO 2011  Winchester, United Kingdom Duration: 30 Aug 2011 → 2 Sept 2011 
Publication series
Name  Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 

Volume  6859 LNCS 
ISSN (Print)  03029743 
ISSN (Electronic)  16113349 
Conference
Conference  4th International Conference on Algebra and Coalgebra in Computer Science, CALCO 2011 

Country/Territory  United Kingdom 
City  Winchester 
Period  30/08/11 → 2/09/11 
Keywords
 Coalgebra
 Lawvere theories
 Lax natural transformations
 Logic programming
 Oplax maps of coalgebras
 SLDresolution
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Dive into the research topics of 'Coalgebraic semantics for derivations in logic programming'. Together they form a unique fingerprint.Projects
 1 Finished

Fellowship CLANN EP/F044046/1: Computational Logic in Artificial Neural Networks
Dyckhoff, R. (PI)
1/10/08 → 30/09/11
Project: Fellowship