Towards World Identification in Description Logics
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Опубликован:
11.01.2023
Ключевые слова:
concept, description Logic, hybridised world description, individual, nomina, nominal, world description, world identification
Main Article Content
Аннотация
The logical analysis of the usability of nominals, that are introduced by Hybrid Logic, informal descriptions of the world (within modern knowledge representation systems and semantic systems) is very important because nominals, as second sorts of propositional symbols, can support logical identification of the described world at specific states. This paper will focus on answering the philosophical-logical question of ‘how a fundamental world description in the description logic (DL) and a nominal can be related to each other?’. Based on my assumption that nominals can support more adequate identification of the world in DL, this paper will deal with the concept of ‘world identification’. Accordingly, based on a logical-terminological analysis of nominals, it will analyse hybridised fundamental world descriptions. Relying on the outcomes, this research will reach the idea that we can have a hybrid description logic with the analysed concepts.
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Как цитировать
Badie F. Towards World Identification in Description Logics // Логические исследования / Logical Investigations. 2023. Т. 28. № 2. C. 115-134.
Выпуск
Раздел
Философская логика
Copyright (c) 2022 Farshad Badie
Это произведение доступно по лицензии Creative Commons «Attribution-NonCommercial» («Атрибуция — Некоммерческое использование») 4.0 Всемирная.
Литература
Areces, 2000 – Areces, C.E. Logic Engineering. The Case of Description and Hybrid Logics, University of Amsterdam: ILLC dissertation series, 2000.
Artale & Franconi, 2000 – Artale, A. & Franconi, E. “A Survey of Temporal Extensions of Description Logics”, Ann. Math. Artif. Intell., 2000, Vol. 30, No. 1–4, pp. 171–210.
Artale et al., 2014 – Artale, A., Kontchakov, R., Ryzhikov, V. & Zakharyaschev, M.“A Cookbook for Temporal Conceptual Data Modelling with Description Logics”, ACM Transactions on Computational Logic, 2014, No. 25, pp. 1–50.
Baader & Hollunder, 1991 – Baader, F. & Hollunder, B. “KRIS: Knowledge Representation and Inference System”, ACM SIGART Bull, 1991, Vol. 2, No. 3, pp. 8–14.
Baader et al., 2003 – Baader, F., K¨usters, R. & Wolter, F. “Extensions to Description Logics”, in: F. Baader, D. Calvanese, D. L. McGuinness, D. Nardi & P.F. PatelSchneider (eds.), Description Logic Handbook, Cambridge University Press, 2003, pp. 219–261.
Baader et al., 2007 – Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D. & PatelSchneider, P.F. The Description Logic Handbook: Theory, Implementation and Applications. Cambridge University Press, 2007.
Baader et al., 2017a – Baader, F., Horrocks, I., Lutz, C. & Sattler, U. An Introduction to Description Logic. Cambridge University Press, 2017.
Baader et al., 2017b – Baader, F., Borgwardt, S., Koopmann, P., Ozaki, A. & Thost, V. “Metric Temporal Description Logics with Interval-Rigid Names”, in: Clare Dixon & Marcelo Finger (eds.), FroCoS. Springer, 2017, pp. 60–76. Baader et al., 2017c – Baader, F., Horrocks, I., Lutz, C., & Sattler, U. “A Basic Description Logic”, in: An Introduction to Description Logic. Cambridge: Cambridge University Press, 2017, pp. 10–49.
Baader et al., 2020 – Baader, F., Borgwardt, S., Koopmann, P., Ozaki, A. & Thost, V. “Metric Temporal Description Logics with Interval-Rigid Names”, ACM Trans. Comput. Log., 2020, Vol. 21, No. 30, pp. 1–46.
Badie, 2017a – Badie F. “From Concepts to Predicates Within Constructivist Epistemology”, in: Baltag A., Seligman J., Yamada T. (eds.), Logic, Rationality, and Interaction, Lecture Notes in Computer Science, Vol. 10455. Springer: Berlin, Heidelberg, 2017, pp. 687–692.
Badie, 2017b – Badie, F. A Theoretical Model for Meaning Construction through Constructivist Concept Learning: A Conceptual, Terminological, Logical and Semantic Study within Human-Human-Machine Interactions, PhD series for the Faculty of Humanities. Aalborg University Press: Aalborg, Denmark, 2017.
Badie, 2018 – Badie, F. “On Logical Characterisation of Human Concept Learning based on Terminological Systems”, Logic And Logical Philosophy, 2018, Vol. 27, No. 4, pp. 545–566.
Badie, 2020 – Badie, F. “Logic and Constructivism: A Model of Terminological Knowledge”, Journal of Knowledge Structures & Systems, 2020, Vol. 1, No. 1, pp. 23–39.
Blackburn, 1993 – Blackburn, P. “Nominal Tense Logic”, Notre Dame J. Formal Logic, 1993, Vol. 34, No. 1, pp. 56–83.
Blackburn, 2006 – Blackburn, P. “Arthur Prior and Hybrid Logic”, Synth, 2006, Vol. 150, No. 3, pp. 329–372.
Blackburn & Jørgensen, 2012 – Blackburn, P. & Jørgensen, K.F. “Indexical Hybrid Tense Logic”, in: T. Bolander, T. Bra¨uner; S. Ghilardi & Lawrence S. Moss (eds.), Advances in Modal Logic. College Publications, 2012, pp. 144–160.
Blackburn & Jørgensen, 2016 – Blackburn, P. & Jørgensen, K.F. “Arthur Prior and ‘Now’”, Synth, 2016, Vol. 193, No. 11, pp. 3665–3676.
Blackburn & Jørgensen, 2016b – Blackburn, P. & Jørgensen, K.F. “Reichenbach, Prior and hybrid tense logic”, Synth, 2016, Vol. 193, No. 11, pp. 3677–3689.
Blackburn & Seligman, 1995 – Blackburn, P. & Seligman, J. “Hybrid Languages”, J. Log. Lang, 1995, Vol. 4, No. 3, pp. 251–272.
Bourgaux et al., 2019 – Bourgaux, C., Koopmann, P. & Turhan, A.-Y. “Ontologymediated Query Answering Over Temporal and Inconsistent Data”, Semantic Web, 2019, Vol. 10, No. 3, pp. 475–521.
Brachman et al., 1983 – Brachman, R., Fikes, R. & Levesque, H. “Krypton: A Functional Approach to Knowledge Representation”, Computer, 1983, Vol. 16–10, pp. 67–73.
Brauner, 2017 – Brauner, T. “Hybrid Logic”, The Stanford Encyclopedia of Philosophy (Summer 2017 Edition), Edward N. Zalta (ed.), 2017, Center for the Study of Language and Information (CSLI), Stanford University.
Goranko & Rumberg, 2020 – Goranko, V. & Rumberg, A. “Temporal Logic”, The Stanford Encyclopedia of Philosophy (Summer 2020 Edition), Edward N. Zalta (ed.), 2020, Center for the Study of Language and Information (CSLI), Stanford University.
Gorin & Schroder, 2012 – Gorin, D. & Schroder, L. “Extending ALCQ with Bounded Self-Reference”, in: T. Bolander, T. Brauner, S. Ghilardi & L.S. Moss (eds.), Advances in Modal Logic. College Publications, 2012, pp. 300–316.
Guarino, 1998 – Guarino, N. “Formal Ontology in Information Systems”, Proceedings of the 1st International Conference (Trento, Italy). IOS Press: Amsterdam, The Netherlands, 1998, pp. 3–15.
Horrocks et al., 2000 – Horrocks, I., Sattler, U. & Tobies, S. “Practical Reasoning for Very Expressive Description Logics”, Logic Journal of the IGPL, 2000, Vol. 8, No. 3, pp. 239–264.
Horrocks & Sattler, 2001 – Horrocks, I. & Sattler, U. “Ontology Reasoning in the SHOQ(D) Description Logic”, in: IJCAI, 2001, pp. 199–204.
Horrocks et al., 2006 – Horrocks, I., Kutz, O. & Sattler, U. “The Even More Irresistible SROIQ”, iIn: P. Doherty, J, Mylopoulos & Ch. A. Welty (eds.), Proc. of the 10th Int. Conf. on Principles of Knowledge Representation and Reasoning. AAAI Press, 2006, pp. 57–67.
Horrocks et al., 2007 – Horrocks, I., Glimm, B. & Sattler, U. “Hybrid Logics and Ontology Languages”, Electron. Notes Theor. Comput. Sci., 2007, Vol. 174, No. 6, pp. 3–14.
Kripke, 1963 – Kripke, S. “Semantical Considerations on Modal Logic”, Acta Phil. Fennica, 1963, Vol. 16, pp. 83–94.
Krotzsch et al., 2011 – Kr¨otzsch, M., Maier, F., Krisnadhi, A.A. & Hitzler, P. “Nominal Schemas for Integrating Rules and Description Logics”, in: R. Rosati, S. Rudolph & M. Zakharyaschev, (eds.), Description Logics, 2011, pp. 268–278.
Lutz et al., 2005 – Lutz, C.; Areces, C., Horrocks, I. & Sattler, U. “Keys, Nominals, and Concrete Domains”, J. Artif. Intell. Res., 2005, Vol. 23, pp. 667–726.
Lutz et al., 2008 – Lutz, C., Wolter, F. & Zakharyaschev, M. “Temporal Description Logics: A Survey”, 15th International Symposium on Temporal Representation and Reasoning, Montreal. QC, Canada, 2008, pp. 3–14.
Menzel, 2018 – Menzel, Ch. “Actualism”, The Stanford Encyclopedia of Philosophy (Summer 2018 Edition), Edward N. Zalta (ed.), 2018, Center for the Study of Language and Information (CSLI), Stanford University.
Minsky, 1975 – Minsky, M. “A Framework for Representing Knowledge”, in: P. Wiston (ed.), The psychology of computer vision. Mc Graw Hill, New York, 1975, pp. 211-277.
Øhrstrøm, 1996 – Øhrstrøm, P. “A Statement of Temporal Realism”, in: B. Jack Copeland (ed.), Logic and Reality, Essays on the Legacy of Arthur Prior. Clarendon Press, 1996, pp. 43–51.
Prior, 1967 – Prior, A.N. Past, Present and Future. Oxford University Press, 1967.
Quillian & Minski, 1968 – Quilian, M.R., Minski, M. “Semantic Memory”, in: M. Minski (ed.), Semantic Information Processing. MIT Press, Cambridge, MA, 1968, pp. 227–270.
Schild, 1993 – Schild, K. “Combining Terminological Logics with Tense Logic”, in: Miguel Filgueiras & Luis Damas (ed.), EPIA. Springer, 1993, pp. 105–120.
Sikos, 2017 – Sikos, L.F. Description Logics in Multimedia Reasoning. Springer, 2017.
Tobies, 2000 – Tobies, S. “The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics”, J. Artif. Intell. Res., 2000, Vol. 12,pp. 199–217.
OWL, 2012 – Web Ontology Language (OWL), [https://www.w3.org/OWL, 2012, accessed on 01.04.2022].
Artale & Franconi, 2000 – Artale, A. & Franconi, E. “A Survey of Temporal Extensions of Description Logics”, Ann. Math. Artif. Intell., 2000, Vol. 30, No. 1–4, pp. 171–210.
Artale et al., 2014 – Artale, A., Kontchakov, R., Ryzhikov, V. & Zakharyaschev, M.“A Cookbook for Temporal Conceptual Data Modelling with Description Logics”, ACM Transactions on Computational Logic, 2014, No. 25, pp. 1–50.
Baader & Hollunder, 1991 – Baader, F. & Hollunder, B. “KRIS: Knowledge Representation and Inference System”, ACM SIGART Bull, 1991, Vol. 2, No. 3, pp. 8–14.
Baader et al., 2003 – Baader, F., K¨usters, R. & Wolter, F. “Extensions to Description Logics”, in: F. Baader, D. Calvanese, D. L. McGuinness, D. Nardi & P.F. PatelSchneider (eds.), Description Logic Handbook, Cambridge University Press, 2003, pp. 219–261.
Baader et al., 2007 – Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D. & PatelSchneider, P.F. The Description Logic Handbook: Theory, Implementation and Applications. Cambridge University Press, 2007.
Baader et al., 2017a – Baader, F., Horrocks, I., Lutz, C. & Sattler, U. An Introduction to Description Logic. Cambridge University Press, 2017.
Baader et al., 2017b – Baader, F., Borgwardt, S., Koopmann, P., Ozaki, A. & Thost, V. “Metric Temporal Description Logics with Interval-Rigid Names”, in: Clare Dixon & Marcelo Finger (eds.), FroCoS. Springer, 2017, pp. 60–76. Baader et al., 2017c – Baader, F., Horrocks, I., Lutz, C., & Sattler, U. “A Basic Description Logic”, in: An Introduction to Description Logic. Cambridge: Cambridge University Press, 2017, pp. 10–49.
Baader et al., 2020 – Baader, F., Borgwardt, S., Koopmann, P., Ozaki, A. & Thost, V. “Metric Temporal Description Logics with Interval-Rigid Names”, ACM Trans. Comput. Log., 2020, Vol. 21, No. 30, pp. 1–46.
Badie, 2017a – Badie F. “From Concepts to Predicates Within Constructivist Epistemology”, in: Baltag A., Seligman J., Yamada T. (eds.), Logic, Rationality, and Interaction, Lecture Notes in Computer Science, Vol. 10455. Springer: Berlin, Heidelberg, 2017, pp. 687–692.
Badie, 2017b – Badie, F. A Theoretical Model for Meaning Construction through Constructivist Concept Learning: A Conceptual, Terminological, Logical and Semantic Study within Human-Human-Machine Interactions, PhD series for the Faculty of Humanities. Aalborg University Press: Aalborg, Denmark, 2017.
Badie, 2018 – Badie, F. “On Logical Characterisation of Human Concept Learning based on Terminological Systems”, Logic And Logical Philosophy, 2018, Vol. 27, No. 4, pp. 545–566.
Badie, 2020 – Badie, F. “Logic and Constructivism: A Model of Terminological Knowledge”, Journal of Knowledge Structures & Systems, 2020, Vol. 1, No. 1, pp. 23–39.
Blackburn, 1993 – Blackburn, P. “Nominal Tense Logic”, Notre Dame J. Formal Logic, 1993, Vol. 34, No. 1, pp. 56–83.
Blackburn, 2006 – Blackburn, P. “Arthur Prior and Hybrid Logic”, Synth, 2006, Vol. 150, No. 3, pp. 329–372.
Blackburn & Jørgensen, 2012 – Blackburn, P. & Jørgensen, K.F. “Indexical Hybrid Tense Logic”, in: T. Bolander, T. Bra¨uner; S. Ghilardi & Lawrence S. Moss (eds.), Advances in Modal Logic. College Publications, 2012, pp. 144–160.
Blackburn & Jørgensen, 2016 – Blackburn, P. & Jørgensen, K.F. “Arthur Prior and ‘Now’”, Synth, 2016, Vol. 193, No. 11, pp. 3665–3676.
Blackburn & Jørgensen, 2016b – Blackburn, P. & Jørgensen, K.F. “Reichenbach, Prior and hybrid tense logic”, Synth, 2016, Vol. 193, No. 11, pp. 3677–3689.
Blackburn & Seligman, 1995 – Blackburn, P. & Seligman, J. “Hybrid Languages”, J. Log. Lang, 1995, Vol. 4, No. 3, pp. 251–272.
Bourgaux et al., 2019 – Bourgaux, C., Koopmann, P. & Turhan, A.-Y. “Ontologymediated Query Answering Over Temporal and Inconsistent Data”, Semantic Web, 2019, Vol. 10, No. 3, pp. 475–521.
Brachman et al., 1983 – Brachman, R., Fikes, R. & Levesque, H. “Krypton: A Functional Approach to Knowledge Representation”, Computer, 1983, Vol. 16–10, pp. 67–73.
Brauner, 2017 – Brauner, T. “Hybrid Logic”, The Stanford Encyclopedia of Philosophy (Summer 2017 Edition), Edward N. Zalta (ed.), 2017, Center for the Study of Language and Information (CSLI), Stanford University.
Goranko & Rumberg, 2020 – Goranko, V. & Rumberg, A. “Temporal Logic”, The Stanford Encyclopedia of Philosophy (Summer 2020 Edition), Edward N. Zalta (ed.), 2020, Center for the Study of Language and Information (CSLI), Stanford University.
Gorin & Schroder, 2012 – Gorin, D. & Schroder, L. “Extending ALCQ with Bounded Self-Reference”, in: T. Bolander, T. Brauner, S. Ghilardi & L.S. Moss (eds.), Advances in Modal Logic. College Publications, 2012, pp. 300–316.
Guarino, 1998 – Guarino, N. “Formal Ontology in Information Systems”, Proceedings of the 1st International Conference (Trento, Italy). IOS Press: Amsterdam, The Netherlands, 1998, pp. 3–15.
Horrocks et al., 2000 – Horrocks, I., Sattler, U. & Tobies, S. “Practical Reasoning for Very Expressive Description Logics”, Logic Journal of the IGPL, 2000, Vol. 8, No. 3, pp. 239–264.
Horrocks & Sattler, 2001 – Horrocks, I. & Sattler, U. “Ontology Reasoning in the SHOQ(D) Description Logic”, in: IJCAI, 2001, pp. 199–204.
Horrocks et al., 2006 – Horrocks, I., Kutz, O. & Sattler, U. “The Even More Irresistible SROIQ”, iIn: P. Doherty, J, Mylopoulos & Ch. A. Welty (eds.), Proc. of the 10th Int. Conf. on Principles of Knowledge Representation and Reasoning. AAAI Press, 2006, pp. 57–67.
Horrocks et al., 2007 – Horrocks, I., Glimm, B. & Sattler, U. “Hybrid Logics and Ontology Languages”, Electron. Notes Theor. Comput. Sci., 2007, Vol. 174, No. 6, pp. 3–14.
Kripke, 1963 – Kripke, S. “Semantical Considerations on Modal Logic”, Acta Phil. Fennica, 1963, Vol. 16, pp. 83–94.
Krotzsch et al., 2011 – Kr¨otzsch, M., Maier, F., Krisnadhi, A.A. & Hitzler, P. “Nominal Schemas for Integrating Rules and Description Logics”, in: R. Rosati, S. Rudolph & M. Zakharyaschev, (eds.), Description Logics, 2011, pp. 268–278.
Lutz et al., 2005 – Lutz, C.; Areces, C., Horrocks, I. & Sattler, U. “Keys, Nominals, and Concrete Domains”, J. Artif. Intell. Res., 2005, Vol. 23, pp. 667–726.
Lutz et al., 2008 – Lutz, C., Wolter, F. & Zakharyaschev, M. “Temporal Description Logics: A Survey”, 15th International Symposium on Temporal Representation and Reasoning, Montreal. QC, Canada, 2008, pp. 3–14.
Menzel, 2018 – Menzel, Ch. “Actualism”, The Stanford Encyclopedia of Philosophy (Summer 2018 Edition), Edward N. Zalta (ed.), 2018, Center for the Study of Language and Information (CSLI), Stanford University.
Minsky, 1975 – Minsky, M. “A Framework for Representing Knowledge”, in: P. Wiston (ed.), The psychology of computer vision. Mc Graw Hill, New York, 1975, pp. 211-277.
Øhrstrøm, 1996 – Øhrstrøm, P. “A Statement of Temporal Realism”, in: B. Jack Copeland (ed.), Logic and Reality, Essays on the Legacy of Arthur Prior. Clarendon Press, 1996, pp. 43–51.
Prior, 1967 – Prior, A.N. Past, Present and Future. Oxford University Press, 1967.
Quillian & Minski, 1968 – Quilian, M.R., Minski, M. “Semantic Memory”, in: M. Minski (ed.), Semantic Information Processing. MIT Press, Cambridge, MA, 1968, pp. 227–270.
Schild, 1993 – Schild, K. “Combining Terminological Logics with Tense Logic”, in: Miguel Filgueiras & Luis Damas (ed.), EPIA. Springer, 1993, pp. 105–120.
Sikos, 2017 – Sikos, L.F. Description Logics in Multimedia Reasoning. Springer, 2017.
Tobies, 2000 – Tobies, S. “The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics”, J. Artif. Intell. Res., 2000, Vol. 12,pp. 199–217.
OWL, 2012 – Web Ontology Language (OWL), [https://www.w3.org/OWL, 2012, accessed on 01.04.2022].