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Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.18 n.3 México Jul./Sep. 2014 

Artículos regulares


Structural Isomorphism of Meaning and Synonymy


Marie Duží


VSB-Technical University Ostrava, Czech Republic.


Article received on 08/01/2014.
On 06/02/2014.



In this paper I am going to deal with the phenomenon of synonymy from the logical point of view. In Transparent Intensional Logic (TIL), which is my background theory, the sense of an expression is an algorithmically structured procedure detailing what operations to apply to what procedural constituents to arrive at the object (if any) denoted by the expression. Such procedures are rigorously defined as TIL constructions. In this new orthodoxy of structured meanings and procedural semantics we encounter the problem of the granularity of procedure individuation. Though the identity of TIL constructions is rigorously defined, they are a bit too fine-grained from the procedural point of view. In an effort to solve the problem we introduced the notion of procedural isomorphism. Any two terms or expressions whose respective meanings are procedurally isomorphic are deemed semantically indistinguishable, hence synonymous and thus substitutable in any context, whether extensional, intensional or hyperintensional. The novel contribution of this paper is a formally worked-out, philosophically motivated criterion of hyperintensional individuation, which is defined in terms of a slightly more carefully formulated version of α-conversion and β-conversion by value, which amounts to a modification of Church's Alternative (A1).

Keywords: Procedural semantics, β-conversion by value, procedural isomorphism, transparent intensional logic, synonymy.





This work has been supported by the internal grant agency of VSB-Technical University Ostrava, Project No. SP2014/157, "Knowledge modeling, process simulation and design".

Versions of this paper have been presented at Logica 2013, Czech Republic, and CICLing 2014, Nepal.



1. Anderson, C.A. (1998). Alonzo Church's contributions to philosophy and intensional logic. The Bulletin of Symbolic Logic, 4(2), 129–171.         [ Links ]

2. Chang, S. & Felleisen, M. (2012). The call-by-need lambda calculus, revisited. Programming Languages and Systems. Lecture Notes in Computer Science, 7211, 128–147.         [ Links ]

3. Carnap, R. (1947). Meaning and necessity. Chicago: Chicago University Press.         [ Links ]

4. Church, A. (1993). A revised formulation of the logic of sense and denotation. Alternative (1). Noûs, 27(2), 141–157.         [ Links ]

5. Duží, M. (2010). The paradox of inference and the non-triviality of analytic information. Journal of Philosophical Logic, 39(5), 473–510.         [ Links ]

6. Duží, M. (2012). Towards an extensional calculus of hyperintensions. Organon F, 19, supplementary issue 1, 20–45.         [ Links ]

7. Duží, M. (2013). Deduction in TIL: From simple to ramified hierarchy of types. Organon F, 20, supplementary issue 2, 5–36.         [ Links ]

8. Duží, M. & Jespersen, B. (2010). Transparent Quantification into Hyperintensional Contexts. In M. Peliš and V. Punčochář (eds.), The Logica Yearbook 2010 (81–98). London: College Publications.         [ Links ]

9. Duží, M. & Jespersen, B. (2012). Transparent quantification into hyperpropositional contexts de re. Logique & Analyse, 55(220), 513–554.         [ Links ]

10. Duží, M. & Jespersen, B. (2013). Procedural isomorphism, analytic information, and β-conversion by value. Logic Journal of the IGPL, 21(2), 291–308.         [ Links ]

11. Duží, M., Jespersen, B. (to appear). Transparent quantification into hyperintensional objectual attitudes. Synthese, special issue on Hyperintensionality.         [ Links ]

12. Duží, M., Jespersen, B., & Materna, P. (2010). Procedural Semantics for Hyperintensional Logic: Foundations and Applications of Trasnsparent Intensional Logic. Dordrecht: New York: Springer.         [ Links ]

13. Ludwig, K. & Ray, G. (1998). Semantics for opaque contexts. Philosophical Perspectives, 12(S12), 141–166.         [ Links ]

14. Materna, P. (1998). Concepts and Objects. Acta Philosophica Fennica, vol. 63. Helsinki: Edidit Societas Philosophica: Distribuit Akateeminen Kirjakauppa.         [ Links ]

15. Moschovakis, Y.N. (1993). Sense and denotation as algorithm and value. Lecture Notes in Logic, 2, 210–249.         [ Links ]

16. Plotkin, G.D. (1975). Call-by-name, call-by-value, and the lambda calculus. Theoretical Computer Science, 1, 125–159.         [ Links ]

17. Salmon, N. (2010). Lambda in sentences with designators: an ode to complex predication. Journal of Philosophy, 107(9), 445–468.         [ Links ]

18. Tichý, P. (1968). Smysl a procedura. Filosofický časopis, 16, 222–232. Translated as 'Sense and procedure' in (Tichý 2004: 77-92).         [ Links ]

19. Tichý, P. (1969). Intensions in terms of Turing machines. Studia Logica, 24(1), 7–21. Reprinted in (Tichý 2004: 93–109).         [ Links ]

20. Tichý, P. (2004). Collected Papers in Logic and Philosophy. Prague: Filosofia; Dunedin, N.Z.: University of Otago Press.         [ Links ]

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