dc.contributor.author | Voutsadakis, George | |
dc.date.accessioned | 2016-03-13T12:21:06Z | |
dc.date.available | 2016-03-13T12:21:06Z | |
dc.date.issued | 2015 | |
dc.identifier.issn | 0138-0680 | |
dc.identifier.uri | http://hdl.handle.net/11089/17400 | |
dc.description.abstract | Wójcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of algebraic and matrix semantics of arbitrary sentential logics. A well-known theorem of Wójcicki asserts that a logic has a referential semantics if and only if it is selfextensional. Referential semantics was subsequently studied in detail by Malinowski and the concept of selfextensionality has played, more recently, an important role in the field of abstract algebraic logic in connection with the operator approach to algebraizability. We introduce and review some of the basic definitions and results pertaining to the referential semantics of π-institutions, abstracting corresponding results from the realm of propositional logics. | pl_PL |
dc.language.iso | en | pl_PL |
dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | pl_PL |
dc.relation.ispartofseries | Bulletin of the Section of Logic;1/2 | |
dc.subject | Referential Logics | pl_PL |
dc.subject | Selfextensional Logics | pl_PL |
dc.subject | Leibniz operator | pl_PL |
dc.subject | Tarski operator | pl_PL |
dc.subject | Suszko operator | pl_PL |
dc.subject | π-institutions | pl_PL |
dc.title | Categorical Abstract Algebraic Logic: Referential π-Institutions | pl_PL |
dc.type | Article | pl_PL |
dc.rights.holder | © Copyright by Uniwersytet Łódzki, Łódź 2015 | pl_PL |
dc.page.number | 33–51 | pl_PL |
dc.contributor.authorAffiliation | School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI 49783, USA. | pl_PL |
dc.identifier.eissn | 2449-836X | |
dc.references | Blok W. J. and Pigozzi D., Algebraizable Logics, Memoirs of the American Mathematical Society, Vol. 77, No. 396 (1989). | pl_PL |
dc.references | Czelakowski J., Equivalential Logics II, Studia Logica, Vol. 40, No. 4 (1981), pp. 355–372. | pl_PL |
dc.references | Czelakowski J., The Suszko Operator Part I, Studia Logica, Vol. 74, No. 1-2 (2003), pp. 181–231. | pl_PL |
dc.references | Czelakowski J., Fregean Logics and the Strong Amalgamation Property, Bulletin of the Section of Logic, Vol. 36, No. 3/4 (2007), pp. 105–116. | pl_PL |
dc.references | Czelakowski J. and Pigozzi D., Amalgamation and Interpolation in Abstract Algebraic Logic, Models, Algebras and Proofs, in Lecture Notes in Pure and Applied Mathematics 203, Dekker, New York, 1999, pp. 187–265. | pl_PL |
dc.references | Czelakowski J. and Pigozzi D., Fregean Logics, Annals of Pure and Applied Logic, Vol. 127, No. 1-3 (2004), pp. 17–76. | pl_PL |
dc.references | Czelakowski J. and Pigozzi D., Fregean Logics with the Multiterm Deduction Theorem and Their Algebraization, Studia Logica, Vol. 78, No. 1-2 (2004), pp. 171–212. | pl_PL |
dc.references | Font J. M. and Jansana R., A General Algebraic Semantics for Sentential Logics, Lecture Notes in Logic, Vol. 332, No. 7 (1996), Springer-Verlag, Berlin Heidelberg, 1996 | pl_PL |
dc.references | Jansana R., Selfextensional Logics in Abstract Algebraic Logic: a Brief Survey, [in:] J.-Y. Béziau, A. Costa-Leite, and A. Facchini, (eds.), Aspects of Universal Logic, Cahiers de Logique, No. 17, Centre de Recerches Sémiologiques, Université de Neuchâtel, Neuchâtel, 2004, pp. 32–65. | pl_PL |
dc.references | Jansana R., Selfextensional Logics with Implication, Béziau, Jean-Yves (ed.), Logica Universalis. Towards a general theory of logic. Basel: Birkh¨auser 2005, pp. 65–88. | pl_PL |
dc.references | Jansana R., Selfextensional Logics with a Conjunction, Studia Logica, Vol. 84, No. 1 (2006), pp. 63–104. | pl_PL |
dc.references | Jansana R. and Palmigiano A., Referential Semantics: Duality and Applications, Reports on Mathematical Logic, Vol. 41 (2006), pp. 63–93. | pl_PL |
dc.references | Malinowski G., A Proof of Ryszard Wójcicki’s Conjecture, Bulletin of the Section of Logic, Vol. 7, No. 1 (1978), pp. 20–25. | pl_PL |
dc.references | Malinowski G., Pseudo-Referential Matrix Semantics for Propositional Logics, Bulletin of the Section of Logic, Vol. 12, No. 3 (1983), pp. 90–98. | pl_PL |
dc.references | Malinowski G., Many-Valued Referential Matrices, Bulletin of the Section of Logic, Vol. 24, No. 3 (1995), pp. 140–146. | pl_PL |
dc.references | Malinowski G., Referentiality and Matrix Semantics, Studia Logica, Vol. 97, No. 2 (2011), pp. 297–312.’ | pl_PL |
dc.references | Marek I., Remarks on Pseudo-Referential Matrices, Bulletin of the Section of Logic, Vol. 16, No. 2 (1987), pp. 89–92. | pl_PL |
dc.references | Pigozzi D., Fregean Algebraic Logic, [in:] H. Andréka, J. Monk, and I. Németi, (eds.), Algebraic Logic, Budapest, 8-14 August, 1988, Colloquia Mathematica Societatis János Bolyai, Vol. 54, North-Holland, Amsterdam, 1991, pp. 473–502. | pl_PL |
dc.references | Tokarz M., Synonymy in Sentential Languages: a Pragmatic View, Studia Logica, Vol. 47, No. 2 (1988), pp. 93–97. | pl_PL |
dc.references | Wójcicki R., Referential Matrix Semantics for Propositional Calculi, Bulletin of the Section of Logic, Vol. 8, No. 4 (1979), pp. 170–176. | pl_PL |
dc.references | Wójcicki R., More About Referential Matrices, Bulletin of the Section of Logic, Vol. 9, No. 2 (1980), pp. 93–95. | pl_PL |
dc.references | Wójcicki R., Theory of Logical Calculi, Basic Theory of Consequence Operations, Vol. 199, Synthese Library, Reidel, Dordrecht, 1988. | pl_PL |
dc.references | Voutsadakis G., Categorical Abstract Algebraic Logic: Models of π-Institutions, Notre Dame Journal of Formal Logic, Vol. 46, No. 4 (2005), pp. 439–460. | pl_PL |
dc.references | Voutsadakis G., Categorical Abstract Algebraic Logic: Full Models, Frege Systems and Metalogical Properties, Reports on Mathematical Logic, Vol. 41 (2006), pp. 31–62. | pl_PL |
dc.references | Voutsadakis G., Categorical Abstract Algebraic Logic: Referential Algebraic Semantics, Studia Logica, Vol. 101, No. 4 (2013), pp. 849–899. | pl_PL |
dc.references | Voutsadakis G., Categorical Abstract Algebraic Logic: Tarski Congruence Systems, Logical Morphisms and Logical Quotients, to appear in the Journal of Pure and Applied Mathematics: Advances and Applications. | pl_PL |
dc.references | Voutsadakis G., Categorical Abstract Algebraic Logic: Selfextensional π-Institutions with Implication, available in http://www.voutsadakis.com/RESEARCH/papers.html | pl_PL |
dc.references | Voutsadakis G., Categorical Abstract Algebraic Logic: Selfextensional π-Institutions with Conjunction, available in http://www.voutsadakis.com/RESEARCH/papers.html. | pl_PL |
dc.contributor.authorEmail | gvoutsad@lssu.edu | pl_PL |
dc.relation.volume | 44 | pl_PL |