Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs
Answer Set Programming (ASP) is a well established logical approach in artificial intelligence that is widely used for knowledge representation and problem solving. Equilibrium logic extends answer set semantics to more general classes of programs and theories. When intertheory relations are studied...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-06-01
|
| Series: | Algorithms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4893/15/6/201 |
| _version_ | 1797490821280301056 |
|---|---|
| author | Jorge Fandinno David Pearce Concepción Vidal Stefan Woltran |
| author_facet | Jorge Fandinno David Pearce Concepción Vidal Stefan Woltran |
| author_sort | Jorge Fandinno |
| collection | DOAJ |
| description | Answer Set Programming (ASP) is a well established logical approach in artificial intelligence that is widely used for knowledge representation and problem solving. Equilibrium logic extends answer set semantics to more general classes of programs and theories. When intertheory relations are studied in ASP, or in the more general form of equilibrium logic, they are usually understood in the form of comparisons of the answer sets or equilibrium models of theories or programs. This is the case for strong and uniform equivalence and their relativised and projective versions. However, there are many potential areas of application of ASP for which query answering is relevant and a comparison of programs in terms of what can be inferred from them may be important. We formulate and study some natural equivalence and entailment concepts for programs and theories that are couched in terms of inference and query answering. We show that, for the most part, these new intertheory relations coincide with their model-theoretic counterparts. We also extend some previous results on projective entailment for theories and for the new connective called <i>fork</i>. |
| first_indexed | 2024-03-10T00:38:32Z |
| format | Article |
| id | doaj.art-a2e2bae8e7e94bf292c756cb042cab3d |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T00:38:32Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-a2e2bae8e7e94bf292c756cb042cab3d2023-11-23T15:13:13ZengMDPI AGAlgorithms1999-48932022-06-0115620110.3390/a15060201Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set ProgramsJorge Fandinno0David Pearce1Concepción Vidal2Stefan Woltran3College of Information Science & Technology, University of Nebraska Omaha, 6001 Dodge St., Omaha, NE 68182, USADepartamento de Inteligencia Artificial, Universidad Politécnica de Madrid, 28040 Madrid, SpainComputer Science and Information Technologies, University of Corunna, 15008 A Coruña, SpainDatabases and Artificial Intelligence Group (E192-02), Institute of Logic and Computation, Technische Universität Wien, 1040 Vienna, AustriaAnswer Set Programming (ASP) is a well established logical approach in artificial intelligence that is widely used for knowledge representation and problem solving. Equilibrium logic extends answer set semantics to more general classes of programs and theories. When intertheory relations are studied in ASP, or in the more general form of equilibrium logic, they are usually understood in the form of comparisons of the answer sets or equilibrium models of theories or programs. This is the case for strong and uniform equivalence and their relativised and projective versions. However, there are many potential areas of application of ASP for which query answering is relevant and a comparison of programs in terms of what can be inferred from them may be important. We formulate and study some natural equivalence and entailment concepts for programs and theories that are couched in terms of inference and query answering. We show that, for the most part, these new intertheory relations coincide with their model-theoretic counterparts. We also extend some previous results on projective entailment for theories and for the new connective called <i>fork</i>.https://www.mdpi.com/1999-4893/15/6/201answer set programmingequilibrium logicintertheory relationsprojective entailmentforks in ASP |
| spellingShingle | Jorge Fandinno David Pearce Concepción Vidal Stefan Woltran Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs Algorithms answer set programming equilibrium logic intertheory relations projective entailment forks in ASP |
| title | Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs |
| title_full | Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs |
| title_fullStr | Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs |
| title_full_unstemmed | Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs |
| title_short | Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs |
| title_sort | comparing the reasoning capabilities of equilibrium theories and answer set programs |
| topic | answer set programming equilibrium logic intertheory relations projective entailment forks in ASP |
| url | https://www.mdpi.com/1999-4893/15/6/201 |
| work_keys_str_mv | AT jorgefandinno comparingthereasoningcapabilitiesofequilibriumtheoriesandanswersetprograms AT davidpearce comparingthereasoningcapabilitiesofequilibriumtheoriesandanswersetprograms AT concepcionvidal comparingthereasoningcapabilitiesofequilibriumtheoriesandanswersetprograms AT stefanwoltran comparingthereasoningcapabilitiesofequilibriumtheoriesandanswersetprograms |