# On Two Notions of Computation in Transparent Intensional Logic

Original Paper

First Online:

- 35 Downloads

## Abstract

In Transparent Intensional Logic we can recognize two distinct notions of computation that loosely correspond to term rewriting and term interpretation as known from lambda calculus. Our goal will be to further explore these two notions and examine some of their properties.

## Keywords

Transparent intensional logic Procedural semantics Lambda calculus Term rewriting Term interpretation## Notes

### Acknowledgements

An earlier version of this paper was presented at the 21st Conference Applications of Logic in Philosophy and the Foundations of Mathematics in Szklarska Porȩba, Poland 2016. I would like to thank all the participants of this conference for their valuable notes and remarks.

## References

- Barendregt Hendrik P (1984) The lambda calculus: its syntax and semantics. North-Holland, AmsterdamGoogle Scholar
- Duží M (2017) If structured propositions are logical procedures then how are procedures individuated? Synthese. https://doi.org/10.1007/s11229-017-1595-5 (
**in press**)Google Scholar - Duží M, Kosterec M (2017) A valid rule of \(\beta \)-conversion for the logic of partial functions. Organon F 24(1):10–36Google Scholar
- Duží M, Jespersen B, Materna P (2010) Procedural semantics for hyperintensional logic: foundations and applications of transparent intensional logic. Springer, DordrechtGoogle Scholar
- Girard J-Y, Taylor P, Lafont Y (1989) Proofs and types. Cambridge University Press, CambridgeGoogle Scholar
- Jespersen B (2017) Anatomy of a proposition. Synthese. https://doi.org/10.1007/s11229-017-1512-y (
**in press**)Google Scholar - Martin-Löf P (1984) Intuitionistic type theory. Bibliopolis, BerkeleyGoogle Scholar
- Materna P (1998) Concepts and objects. Philosophical Society of Finland, HelsinkiGoogle Scholar
- Materna P (2013) Equivalence of problems (an attempt at an explication of problem). Axiomathes 23(4):617–631. https://doi.org/10.1007/s10516-012-9201-4 CrossRefGoogle Scholar
- Moschovakis YN (2006) A logical calculus of meaning and synonymy. Linguist Philos 29(1):27–89. https://doi.org/10.1007/s10988-005-6920-7 CrossRefGoogle Scholar
- Muskens R (2005) Sense and the computation of reference. Linguist Philos 28(4):473–504. https://doi.org/10.1007/s10988-004-7684-1 CrossRefGoogle Scholar
- Pezlar I (2017) Algorithmic theories of problems. A constructive and a non-constructive approach. Log Log Philos 26(4):473–508. https://doi.org/10.12775/LLP.2017.010 Google Scholar
- Primiero G, Jespersen B (2010) Two kinds of procedural semantics for privative modification. Lect Notes Artif Intell 6284:251–271Google Scholar
- Raclavský J (2003) Executions vs. constructions. Logica et Methodologica 7:63–72Google Scholar
- Raclavský J, Kuchyňka P, Pezlar I (2015) Transparentní intenzionální logika jako characteristica universalis a calculus ratiocinator. Masaryk University Press (Munipress), BrnoGoogle Scholar
- Sierszulska A (2006) On Tichý’s determiners and Zalta’s abstract objects. Axiomathes 16(4):486–498. https://doi.org/10.1007/s10516-006-0002-5 CrossRefGoogle Scholar
- Tichý P (1988) The foundations of Frege’s logic. de Gruyter, BerlinCrossRefGoogle Scholar
- van Heijenoort J (1977) From Frege to Gödel: a source book in mathematical logic, 1879–1931. Harvard University Press, CambridgeGoogle Scholar

## Copyright information

© Springer Nature B.V. 2018