TY - CHAP
T1 - Coalgebraic semantics for derivations in logic programming
AU - Komendantskaya, Ekaterina
AU - Power, John
PY - 2011
Y1 - 2011
N2 - Every variable-free logic program induces a Pf 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 variable-free logic program with a Pf P f -coalgebra on Set and showed that, if C(Pf P f ) is the cofree comonad on Pf P f , then given a logic program P qua Pf P f -coalgebra, the corresponding C(Pf P f )-coalgebra structure describes the parallel and-or 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 Poset-valued 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
AB - Every variable-free logic program induces a Pf 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 variable-free logic program with a Pf P f -coalgebra on Set and showed that, if C(Pf P f ) is the cofree comonad on Pf P f , then given a logic program P qua Pf P f -coalgebra, the corresponding C(Pf P f )-coalgebra structure describes the parallel and-or 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 Poset-valued 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
UR - http://dx.doi.org/10.1007/978-3-642-22944-2_19
U2 - 10.1007/978-3-642-22944-2_19
DO - 10.1007/978-3-642-22944-2_19
M3 - Chapter or section
SN - 978-3-22943-5
T3 - Lecture Notes in Computer Science
SP - 268
EP - 282
BT - Algebra and Coalgebra in Computer Science: 4th International Conference, CALCO 2011, Winchetser, UK, August 30 - September 2, 2011. Proceedings
A2 - Corradini, Andrea
A2 - Kin, Bartek
A2 - Cirstea, Corina
PB - Springer
CY - Heidelberg
T2 - 4th International Conference on Algebra and Coalgebra in Computer Science
Y2 - 30 August 2011 through 2 September 2011
ER -