{"type":"ScholarlyArticle","title":"A Tractable, Expressive, and Eventually Complete First-Order Logic of Limited Belief","authors":[{"name":"Gerhard Lakemeyer","slug":"gerhard-lakemeyer","given":"Gerhard","family":"Lakemeyer","affiliation":"Dept. of Computer Science , RWTH Aachen University , Germany"},{"name":"Hector J. Levesque","slug":"hector-j-levesque","given":"Hector J.","family":"Levesque","affiliation":"Dept. of Computer Science , University of Toronto , Canada"}],"abstract":"In knowledge representation, obtaining a notion of belief which is tractable, expressive, and eventually complete has been a somewhat elusive goal. Expressivity here means that an agent should be able to hold arbitrary beliefs in a very expressive language like that of first-order logic, but without being required to perform full logical reasoning on those beliefs. Eventual completeness means that any logical consequence of what is believed will eventually come to be believed, given enough reasoning effort. Tractability in a first-order setting has been a research topic for many years, but in most cases limitations were needed on the form of what was believed, and eventual completeness was so far restricted to the propositional case. In this paper, we propose a novel logic of limited belief, which has all three desired properties.","doi":"10.24963/ijcai.2019/244","url":"https://ijcai.org/proceedings/2019/244","pdf":"https://ijcai.org/proceedings/2019/0244.pdf","markdown":"https://ijcai.org/proceedings/2019/244.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/244","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":244,"pages":{"first":1764,"last":1771},"keywords":["Knowledge Representation and Reasoning: Reasoning about Knowlege and Belief","Knowledge Representation and Reasoning: Computational Complexity of Reasoning","Knowledge Representation and Reasoning: Logics for Knowledge Representation"],"videos":[],"references":[{"position":1,"raw":"[Anderson and Belnap, 1975] A.R. Anderson and N.D. Bel- nap. Entailment: The Logic of Relevance and Necessity. Princeton University Press, 1975.","title":"Entailment: The Logic of Relevance and Necessity","authors":"A R Anderson, N D Belnap","year":"1975","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Buss, 1998] S.R. Buss, An Introduction to Proof Theory. In S.R. Buss (Ed.), Handbook of Proof Theory, Elsevier, 1998.","title":"An Introduction to Proof Theory","authors":"S R Buss","year":"1998","venue":"Handbook of Proof Theory","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Chellas, 1980] B. Chellas, Modal Logic: An Introduction. Cambridge University Press, Cambridge, 1980.","title":"Modal Logic: An Introduction","authors":"B Chellas","year":"1980","venue":null,"doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Cadoli and Schaerf, 1996] M. Cadoli and M. Schaerf. On the complexity of entailment in propositional multivalued logics. Annals of Mathematics and Artificial Intelligence, 18(1):29-50, 1996.","title":"On the complexity of entailment in propositional multivalued logics","authors":"M Cadoli, M Schaerf","year":"1996","venue":"Annals of Mathematics and Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Crawford and Etherington, 1998] J.M. Crawford and D. Etherington. A non-deterministic semantics for tractable inference. In Proc. of AAAI-98, 286-291, 1998.","title":"A non-deterministic semantics for tractable inference","authors":"J M Crawford, D Etherington","year":"1998","venue":"Proc. of AAAI-98","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Dalal, 1996] M. Dalal. Semantics of an anytime family of reasoners. In Proc. of the 12th European Conference on Artificial Intelligence (ECAI-96), pages 360-364, 1996.","title":"Semantics of an anytime family of reasoners","authors":"M","year":"1996","venue":"Proc. of the 12th European Conference on Artificial Intelligence (ECAI-96)","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[D'Agostino, 2015] M. D'Agostino. An informational view of classical logic. Theor. Comput. Sci. 606, 79-97, 2015.","title":"An informational view of classical logic","authors":"M D Agostino","year":"2015","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Delgrande, 1995] J.P. Delgrande. A framework for logics of explicit belief. Computational Intelligence, 11(1):47-88, 1995.","title":"A framework for logics of explicit belief","authors":"J P Delgrande","year":"1995","venue":"Computational Intelligence","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Dunn, 1976] J.M. Dunn. Intuitive semantics for first-degree entailments and coupled trees. Philosophical Studies, 29:149-168, 1976.","title":"Intuitive semantics for first-degree entailments and coupled trees","authors":"J M Dunn","year":"1976","venue":"Philosophical Studies","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Fagin et al., 1990] R. Fagin, J.Y. Halpern, and M.Y. Vardi. A nonstandard approach to the logical omniscience prob- lem. In Proc. of the 3rd Conference on Theoretical Aspects of Reasoning about Knowledge (TARK-90), pages 41-55, 1990.","title":"A nonstandard approach to the logical omniscience problem","authors":"R Fagin, J Y Halpern, M Y Vardi","year":"1990","venue":"Proc. of the 3rd Conference on Theoretical Aspects of Reasoning about Knowledge (TARK-90)","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Frisch, 1987] A. Frisch. Inference without chaining. In Proc. of IJCAI-87, pages 515-519, 1987.","title":"Inference without chaining","authors":"A Frisch","year":"1987","venue":"Proc. of IJCAI-87","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Halpern and Moses, 1992] J.Y. Halpern and Y. Moses. A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence, 54(3):319- 379, 1992.","title":"A guide to completeness and complexity for modal logics of knowledge and belief","authors":"J Y Halpern, Y Moses","year":"1992","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Hintikka, 1962] J. Hintikka. Knowledge and Belief. Cornell University Press, 1962.","title":"Knowledge and Belief","authors":"J Hintikka","year":"1962","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Hintikka, 1973] J. Hintikka. Logic, Language Games and Information. Kantian themes in the philosophy of logic. Clarendon Press, Oxford, 1973.","title":"Logic, Language Games and Information. Kantian themes in the philosophy of logic","authors":"J Hintikka","year":"1973","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Hintikka, 1975] J. Hintikka. Impossible Possible Worlds Vindicated. Journal of Philosophical Logic, 4, 475-484, 1975.","title":"Impossible Possible Worlds Vindicated","authors":"J Hintikka","year":"1975","venue":"Journal of Philosophical Logic","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Klassen et al., 2015] T.Q. Klassen, S.A. McIlraith, and H.J. Levesque, Towards Tractable Inference for Resource- Bounded Agents. AAAI Spring Symposium on Logi- cal Formalizations of Commonsense Reasoning, 89-95, AAAI Press, 2015.","title":"Towards Tractable Inference for Resource-Bounded Agents","authors":"T Q Klassen, S A Mcilraith, H J Levesque","year":"2015","venue":"AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Kripke, 1959] S. Kripke. A completeness theorem in modal logic. Journal of Symbolic Logic, 24:1-14, 1959.","title":"A completeness theorem in modal logic","authors":"S Kripke","year":"1959","venue":"Journal of Symbolic Logic","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Lakemeyer, 1996] G. Lakemeyer. Limited Reasoning in First-Order Knowledge Bases with Full Introspection Ar- tif. Intell. 84(1-2): 209-255, 1996.","title":"Limited Reasoning in First-Order Knowledge Bases with Full Introspection Artif","authors":"G Lakemeyer","year":"1996","venue":"Intell","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Lakemeyer and Levesque, 2013] G. Lakemeyer and H.J. Levesque, Decidable Reasoning in a Logic of Limited Be- lief with Introspection and Unknown Individuals. 23rd In- ternational Joint Conference on Artificial Intelligence (IJ- CAI), 2013.","title":"Decidable Reasoning in a Logic of Limited Belief with Introspection and Unknown Individuals","authors":"G Lakemeyer, H J Levesque","year":"2013","venue":"23rd International Joint Conference on Artificial Intelligence (IJ-CAI)","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Lakemeyer and Levesque, 2014] G. Lakemeyer and H.J. Levesque, Decidable Reasoning in a Fragment of the Epis- temic Situation Calculus. Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-14), Vi- enna, 2014.","title":"Decidable Reasoning in a Fragment of the Epistemic Situation Calculus","authors":"G Lakemeyer, H J Levesque","year":"2014","venue":"Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-14)","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Lakemeyer and Levesque, 2016] G. Lakemeyer and H.J. Levesque. Decidable Reasoning in a Logic of Limited Belief with Function Symbols. In Proc of KR-16, pages 288-297, 2016.","title":"Decidable Reasoning in a Logic of Limited Belief with Function Symbols","authors":"G Lakemeyer, H J Levesque","year":"2016","venue":"Proc of KR-16","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Levesque, 1984] H.J. Levesque. A logic of implicit and ex- plicit belief. In Proc. of AAAI-84, pages 198-202, 1984.","title":"A logic of implicit and explicit belief","authors":"H J Levesque","year":"1984","venue":"Proc. of AAAI-84","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Levesque, 1990] H.J. Levesque, All I know: a study in autoepistemic logic. Artificial Intelligence 42, 263-309, 1990.","title":"All I know: a study in autoepistemic logic","authors":"H J Levesque","year":"1990","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Levesque, 1998] H.J. Levesque. A completeness result for reasoning with incomplete first-order knowledge bases. In Proc. KR-98, pages 14-23, 1998.","title":"A completeness result for reasoning with incomplete first-order knowledge bases","authors":"H J Levesque","year":"1998","venue":"Proc. KR-98","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Levesque and Lakemeyer, 2001] H.J. Levesque and G. Lakemeyer. The Logic of Knowledge Bases. MIT Press, 2001.","title":"The Logic of Knowledge Bases","authors":"H J Levesque, G Lakemeyer","year":"2001","venue":null,"doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Liu et al., 2004] Y. Liu, G. Lakemeyer, and H.J. Levesque. A Logic of Limited Belief for Reasoning with Disjunctive Information. Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR), 587-597, 2004.","title":"A Logic of Limited Belief for Reasoning with Disjunctive Information","authors":"Y Liu, G Lakemeyer, H J Levesque","year":"2004","venue":"Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR)","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Liu and Levesque, 2003] Y. Liu and H.J. Levesque. A tractability result for reasoning with incomplete first-order knowledge bases. In Proc. of IJCAI-03, pages 83-88, 2003.","title":"A tractability result for reasoning with incomplete first-order knowledge bases","authors":"Y Liu, H J Levesque","year":"2003","venue":"Proc. of IJCAI-03","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Liu and Levesque, 2005] Y. Liu and H.J. Levesque. Tractable reasoning in first-order knowledge bases with disjunctive information. In Proc. of the Twentieth National Conference on Artificial Intelligence (AAAI-05), 2005.","title":"Tractable reasoning in first-order knowledge bases with disjunctive information","authors":"Y Liu, H J Levesque","year":"2005","venue":"Proc. of the Twentieth National Conference on Artificial Intelligence (AAAI-05)","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[McCarthy, 1963] J. McCarthy, Programs with common sense. M. Minsky (ed.), Semantic Information Process- ing, MIT Press, Cambridge, 403-418, 1963.","title":"Programs with common sense","authors":"J Mccarthy","year":"1963","venue":"Semantic Information Processing","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Patel-Schneider, 1985] P. Patel-Schneider. A decidable first-order logic for knowledge representation. In Proc. of IJCAI-85, pages 455-458, 1985.","title":"A decidable first-order logic for knowledge representation","authors":"P Patel-Schneider","year":"1985","venue":"Proc. of IJCAI-85","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Schwering, 2017] C. Schwering. A Reasoning System for a First-Order Logic of Limited Belief. In Proc. of IJCAI-17, pages 1247-1253, 2017.","title":"A Reasoning System for a First-Order Logic of Limited Belief","authors":"C Schwering","year":"2017","venue":"Proc. of IJCAI-17","doi":null,"url":null,"internal_url":"/proceedings/2017/173"}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}