Abstract:
In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Information Friendly (IF) logics. In this work we propose an alternative formalization under which invariance with respect the renaming of bound variables is restored. We show that, when one restricts to formulas where each variable is bound only once, our semantics coincide with those previously used in the literature. We also prove basic metatheoretical results of the resulting logic, such as compositionality and truth preserving operations on valuations. We work on Hodges' slash logic (from which results can be easily transferred to other IF-like logics) and we also consider his flattening operator, for which we give a game-theoretical semantics. © 2008 Springer-Verlag Berlin Heidelberg.
Registro:
Documento: |
Artículo
|
Título: | On the formal semantics of IF-like logics |
Autor: | Figueira, S.; Gorín, D.; Grimson, R. |
Ciudad: | Edinburgh |
Filiación: | Departamento de Computación, FCEyN, Universidad de Buenos Aires, Argentina Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Argentina Hasselt University, Transnational University of Limburg CONICET, Argentina
|
Palabras clave: | Canning; Game theory; Information theory; Linguistics; Semantics; Bound variables; Classical logics; Compositionality; Formal Semantics; Heidelberg (CO); International (CO); Fuzzy logic |
Año: | 2008
|
Volumen: | 5110 LNAI
|
Página de inicio: | 164
|
Página de fin: | 178
|
DOI: |
http://dx.doi.org/10.1007/978-3-540-69937-8_15 |
Título revista: | 15th International Workshop on Logic, Language, Information and Computation, WoLLIC 2008
|
Título revista abreviado: | Lect. Notes Comput. Sci.
|
ISSN: | 03029743
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03029743_v5110LNAI_n_p164_Figueira |
Referencias:
- Barendregt, H., The Lambda Calculus: Its syntax and semantics (1985) Studies in logic and the foundations of mathematics, 103. , 2nd edn, North Holland, Amsterdam
- Barwise, J., On branching quantifiers in English (1979) Journal of Philosophical Logic, 8, pp. 47-80
- Caicedo, X., Dechesne, F., Jansen, T.M.V., Equivalence and quantifier rules for logic with imperfect information (2007) Prepublication Series PP, 2007 -20. , ILLC
- Caicedo, X., Krynicki, M., Quantifiers for reasoning with imperfect information and Σ11-logic (1999) Contemporary Mathematics, 235, pp. 17-31
- de Bruijn, N.G., Lambda calculus notation with nameless dummies. A tool for automatic formula manipulation with application to the Church-Rosser theorem (1972) Indagationes Mathematicae, 34, pp. 381-392
- Dechesne, F., (2005) Game, Sets, Maths: Formal investigations into logic with imperfect information, , PhD thesis, Department of Philosophy, University of Tilburg, The Netherlands
- Enderton, H., Finite partially ordered quantifiers (1970) Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 16, pp. 393-397
- Henkin, L., Some remarks on infinitely long formulas (1961) Infinitistic Methods: Proceedings of the Symposium on Foundations of Mathematics, pp. 167-183. , Pergamon Press, Oxford
- Hintikka, J., (1996) The Principles of Mathematics Revisited, , Cambridge University Press, Cambridge
- Hintikka, J., Sandu, G., Game-theoretical semantics (1997) Handbook of logic and language, , van Benthem, J, ter Meulen, A, eds, ch. 6. MIT Press, Cambridge
- Hodges, W., Compositional semantics for a language of imperfect information (1997) Logic Journal of the IGPL, 5 (4)
- Hodges, W., Logics of imperfect information: Why sets of assignments? (2005) Proceedings of the 7th Augustus de Morgan Workshop Interactive Logic: Games and Social Software
- Hodges, W., Some strange quantifiers (1997) LNCS, 1261, pp. 51-65. , Mycielski, J, Rozenberg, G, Salomaa, A, eds, Structures in Logic and Computer Science, Springer, Heidelberg
- Janssen, T.M.V., Independent choices and the interpretation of IF logic (2002) Journal of Logic, Language and Information, 11 (3), pp. 367-387
- Janssen, T.M.V., Dechesne, F., Signalling in IF games: A tricky business (2006) The age of alternative logics, pp. 221-241. , ch. 15, pp, Springer, Heidelberg
- Walkoe Jr., W., Finite partially-ordered quantification (1970) Journal of Symbolic Logic, 35 (4), pp. 535-555
Citas:
---------- APA ----------
Figueira, S., Gorín, D. & Grimson, R.
(2008)
. On the formal semantics of IF-like logics. 15th International Workshop on Logic, Language, Information and Computation, WoLLIC 2008, 5110 LNAI, 164-178.
http://dx.doi.org/10.1007/978-3-540-69937-8_15---------- CHICAGO ----------
Figueira, S., Gorín, D., Grimson, R.
"On the formal semantics of IF-like logics"
. 15th International Workshop on Logic, Language, Information and Computation, WoLLIC 2008 5110 LNAI
(2008) : 164-178.
http://dx.doi.org/10.1007/978-3-540-69937-8_15---------- MLA ----------
Figueira, S., Gorín, D., Grimson, R.
"On the formal semantics of IF-like logics"
. 15th International Workshop on Logic, Language, Information and Computation, WoLLIC 2008, vol. 5110 LNAI, 2008, pp. 164-178.
http://dx.doi.org/10.1007/978-3-540-69937-8_15---------- VANCOUVER ----------
Figueira, S., Gorín, D., Grimson, R. On the formal semantics of IF-like logics. Lect. Notes Comput. Sci. 2008;5110 LNAI:164-178.
http://dx.doi.org/10.1007/978-3-540-69937-8_15