Equilibrium Semantics and Strong Equivalence for Higher-Order Logic Programs
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917556022935552 |
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| author | Charalambidis, Angelos Chatziagapis, Giannos Kostopoulos, Babis Rondogiannis, Panos |
| author_facet | Charalambidis, Angelos Chatziagapis, Giannos Kostopoulos, Babis Rondogiannis, Panos |
| contents | One of the most significant achievements of equilibrium logic was the characterization of strong equivalence, a property crucial for program transformation and optimization in Answer Set Programming (ASP). While ASP has recently been extended to a higher-order setting to enhance its expressive power, the lack of a comparable purely logical foundation has made verifying strong equivalence for higher-order programs or even proving the correctness of simple program transformations, a difficult challenge. This paper addresses this gap by developing a logical semantics for higher-order ASP by extending the equilibrium logic framework. Within this extended framework we demonstrate that every stratified higher-order logic program possesses a unique equilibrium model. Moreover, we establish definability results demonstrating that the syntax of our higher-order language is sufficiently expressive to capture its semantic domains. Finally, and most importantly, we generalize the classical theorem of strong equivalence to the higher-order setting: we prove that two programs are strongly equivalent if and only if they share the same higher-order models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02387 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equilibrium Semantics and Strong Equivalence for Higher-Order Logic Programs Charalambidis, Angelos Chatziagapis, Giannos Kostopoulos, Babis Rondogiannis, Panos Logic in Computer Science One of the most significant achievements of equilibrium logic was the characterization of strong equivalence, a property crucial for program transformation and optimization in Answer Set Programming (ASP). While ASP has recently been extended to a higher-order setting to enhance its expressive power, the lack of a comparable purely logical foundation has made verifying strong equivalence for higher-order programs or even proving the correctness of simple program transformations, a difficult challenge. This paper addresses this gap by developing a logical semantics for higher-order ASP by extending the equilibrium logic framework. Within this extended framework we demonstrate that every stratified higher-order logic program possesses a unique equilibrium model. Moreover, we establish definability results demonstrating that the syntax of our higher-order language is sufficiently expressive to capture its semantic domains. Finally, and most importantly, we generalize the classical theorem of strong equivalence to the higher-order setting: we prove that two programs are strongly equivalent if and only if they share the same higher-order models. |
| title | Equilibrium Semantics and Strong Equivalence for Higher-Order Logic Programs |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2606.02387 |