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 -