We define a novel, extensional, three-valued semantics for higher-orderlogic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic funct...
详细信息
We define a novel, extensional, three-valued semantics for higher-orderlogic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of the type hierarchy. We prove that there exists a bijection between such Fitting-monotonic functions and pairs of two-valued-result functions where the first member of the pair is monotone-antimonotone and the second member is antimonotone-monotone. By deriving an extension of consistent approximation fixpoint theory (Denecker et al. 2004) and utilizing the above bijection, we define an iterative procedure that produces for any given higher-orderlogic program a distinguished extensional model. We demonstrate that this model is actually a minimal one. Moreover, we prove that our construction generalizes the familiar well-founded semantics for classical logic programs, making in this way our proposal an appealing formulation for capturing the well-founded semantics for higher-orderlogic programs.
We define a novel, extensional, three-valued semantics for higher-orderlogic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic funct...
详细信息
We define a novel, extensional, three-valued semantics for higher-orderlogic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of the type hierarchy. We prove that there exists a bijection between such Fitting-monotonic functions and pairs of two-valued-result functions where the first member of the pair is monotone-antimonotone and the second member is antimonotone-monotone. By deriving an extension of consistent approximation fixpoint theory (Denecker et al. 2004) and utilizing the above bijection, we define an iterative procedure that produces for any given higher-orderlogic program a distinguished extensional model. We demonstrate that this model is actually a minimal one. Moreover, we prove that our construction generalizes the familiar well-founded semantics for classical logic programs, making in this way our proposal an appealing formulation for capturing the well-founded semantics for higher-orderlogic programs.
We develop an extensional semantics for higher-orderlogic programs with negation, generalizing the technique that was introduced in [2, 3] for positive higher-order programs. In this way we provide an alternative ext...
详细信息
We develop an extensional semantics for higher-orderlogic programs with negation, generalizing the technique that was introduced in [2, 3] for positive higher-order programs. In this way we provide an alternative extensional semantics for higher-orderlogic programs with negation to the one proposed in [6]. We define for the language we consider the notions of stratification and local stratification, which generalize the familiar such notions from classical logicprogramming, and we demonstrate that for stratified and locally stratified higher-orderlogic programs, the proposed semantics never assigns the unknown truth value. We conclude the paper by providing a negative result: we demonstrate that the well-known stable model semantics of classical logicprogramming, if extended according to the technique of [2, 3] to higher-orderlogic programs, does not in general lead to extensional stable models.
暂无评论