The Stable Model Semantics for Higher-Order Logic Programming
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arXiv
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| Format: | Preprint |
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2024
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| author | Bogaerts, Bart Charalambidis, Angelos Chatziagapis, Giannos Kostopoulos, Babis Pollaci, Samuele Rondogiannis, Panos |
| author_facet | Bogaerts, Bart Charalambidis, Angelos Chatziagapis, Giannos Kostopoulos, Babis Pollaci, Samuele Rondogiannis, Panos |
| contents | We propose a stable model semantics for higher-order logic programs. Our semantics is developed using Approximation Fixpoint Theory (AFT), a powerful formalism that has successfully been used to give meaning to diverse non-monotonic formalisms. The proposed semantics generalizes the classical two-valued stable model semantics of (Gelfond and Lifschitz 1988) as-well-as the three-valued one of (Przymusinski 1990), retaining their desirable properties. Due to the use of AFT, we also get for free alternative semantics for higher-order logic programs, namely supported model, Kripke-Kleene, and well-founded. Additionally, we define a broad class of stratified higher-order logic programs and demonstrate that they have a unique two-valued higher-order stable model which coincides with the well-founded semantics of such programs. We provide a number of examples in different application domains, which demonstrate that higher-order logic programming under the stable model semantics is a powerful and versatile formalism, which can potentially form the basis of novel ASP systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10563 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Stable Model Semantics for Higher-Order Logic Programming Bogaerts, Bart Charalambidis, Angelos Chatziagapis, Giannos Kostopoulos, Babis Pollaci, Samuele Rondogiannis, Panos Logic in Computer Science Artificial Intelligence Programming Languages I.2.3; I.2.5; F.3.2 We propose a stable model semantics for higher-order logic programs. Our semantics is developed using Approximation Fixpoint Theory (AFT), a powerful formalism that has successfully been used to give meaning to diverse non-monotonic formalisms. The proposed semantics generalizes the classical two-valued stable model semantics of (Gelfond and Lifschitz 1988) as-well-as the three-valued one of (Przymusinski 1990), retaining their desirable properties. Due to the use of AFT, we also get for free alternative semantics for higher-order logic programs, namely supported model, Kripke-Kleene, and well-founded. Additionally, we define a broad class of stratified higher-order logic programs and demonstrate that they have a unique two-valued higher-order stable model which coincides with the well-founded semantics of such programs. We provide a number of examples in different application domains, which demonstrate that higher-order logic programming under the stable model semantics is a powerful and versatile formalism, which can potentially form the basis of novel ASP systems. |
| title | The Stable Model Semantics for Higher-Order Logic Programming |
| topic | Logic in Computer Science Artificial Intelligence Programming Languages I.2.3; I.2.5; F.3.2 |
| url | https://arxiv.org/abs/2408.10563 |