Öz
Bu çalışmada Sezgisel Önermeler Lojiği (IPL) için üç semantik sunuyoruz; yani Kripke semantiği, Heyting semantiği ve topolojik semantik. IPL’nin bu semantiklere göre sağlam ve tam olduğunu gösteriyoruz.
Anahtar Kelimeler
Sezgisel lojik Kripke semantiği modal lojik Heyting cebirleri topolojik semantik
Kaynakça
- Bezhanishvili, N. ve de Jong, D., Intuitionistic Logic, ILLC, Universiteit van Amsterdam, (2010).
- Brown, C. E., Semantics of intuitionistic propositional logic, Heyting algebras and Kripke models, (2014).
- Kato, T., Boolean algebra and Propositional Logic, June 23, (2015).
- Kojima, K., Relational and neighborhood semantics for intuitionistic modal logic, Reports on Mathematical Modal Logic, 47, 87-113, (2012).
- Kuznetsov, S., Lecture Notes on Logic, University of Pennsylvania, (2017).
- McKinsey, J.C.C. ve Tarski, A., The algebra of topology, Annals of Mathematics, 141-191, (1944).
- Moniri, M. ve Maleki, F.S, Neighborhood semantics for basic and ıntuitionistic logic, Logic and Logical Philosophy, 24, 334-355, (2015).
- Palmgren, E., Semantics of Intuitionistic Propositional Logic, Lecture Notes for Applied Logic, Dept. of Math. Uppsala University, (2009).
- Troelstra, A.S. ve van Dalen, D., Constructivism in Mathematics: An Introduction, Volume 2, North-Holland, (1988).
- Van Dalen, D., Logic and Structure, Springer, (2012).
- Witczak, T., Intuitionistic modal logic based on neighborhood semantics without superset axiom, arXiv:1707.03859v2[math L0], (2017).
Öz
In this study we present three semantics for Intuitionistic Propositional Logic (IPL); namely, Kripke semantics, Heyting semantics, and topological semantics. We show that IPL is sound and complete with respect to these semantics.
Anahtar Kelimeler
Intuitionistic logic Kripke semantics modal logic Heyting algebras topologic semantics
Kaynakça
- Bezhanishvili, N. ve de Jong, D., Intuitionistic Logic, ILLC, Universiteit van Amsterdam, (2010).
- Brown, C. E., Semantics of intuitionistic propositional logic, Heyting algebras and Kripke models, (2014).
- Kato, T., Boolean algebra and Propositional Logic, June 23, (2015).
- Kojima, K., Relational and neighborhood semantics for intuitionistic modal logic, Reports on Mathematical Modal Logic, 47, 87-113, (2012).
- Kuznetsov, S., Lecture Notes on Logic, University of Pennsylvania, (2017).
- McKinsey, J.C.C. ve Tarski, A., The algebra of topology, Annals of Mathematics, 141-191, (1944).
- Moniri, M. ve Maleki, F.S, Neighborhood semantics for basic and ıntuitionistic logic, Logic and Logical Philosophy, 24, 334-355, (2015).
- Palmgren, E., Semantics of Intuitionistic Propositional Logic, Lecture Notes for Applied Logic, Dept. of Math. Uppsala University, (2009).
- Troelstra, A.S. ve van Dalen, D., Constructivism in Mathematics: An Introduction, Volume 2, North-Holland, (1988).
- Van Dalen, D., Logic and Structure, Springer, (2012).
- Witczak, T., Intuitionistic modal logic based on neighborhood semantics without superset axiom, arXiv:1707.03859v2[math L0], (2017).
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Mühendislik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Aralık 2018 |
| Gönderilme Tarihi | 3 Nisan 2018 |
| Yayımlandığı Sayı | Yıl 2018 Cilt: 20 Sayı: 2 |