Algorithmic Theories of Problems. A Constructive and a Non-Constructive Approach
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | Logic and Logical Philosophy |
| MU Faculty or unit | |
| Citation | |
| Web | http://apcz.umk.pl/czasopisma/index.php/LLP/article/view/LLP.2017.010 |
| Doi | http://dx.doi.org/10.12775/LLP.2017.010 |
| Field | Philosophy and religion |
| Keywords | logic of problems; algorithmic semantics; procedural semantics; Constructive Type Theory; Transparent Intensional Logic |
| Description | In this paper we examine two approaches to the formal treatment of the notion of problem in the paradigm of algorithmic semantics. Namely, we will explore an approach based on Martin-Löf’s Constructive Type Theory (CTT), which can be seen as a direct continuation of Kolmogorov’s original calculus of problems, and an approach utilizing Tichý’s Transparent Intensional Logic (TIL), which can be viewed as a non-constructive attempt of interpreting Kolmogorov’s logic of problems. In the last section we propose Kolmogorov and CTT-inspired modifications to TIL-based approach. The focus will be on non-empirical (i.e., mathematical and logical) problems only. |
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