Logical Approach to Programming

Nepeivoda, N. N.

doi:10.1016/s0049-237x(09)70185-5

Cited by 3 publications

(1 citation statement)

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“…If C is a Harrop formula in the context Γ then there exists a proof object f (z) such Γ, z : C | f (z) : C. 25 24 In this paper, we are solely interested in the variant of the Split rule where C is a Harrop formula, however, it might be interesting to consider also different variants. For example, a variant where C is an almost negative formula (Troelstra (1973)), or a normal formula (Nepeivoda (1978), Nepeivoda (1982)), or a singleton formula (Sasaki (1986)), or a rank 0 formula (Hayashi and Nakano (1988)) that generalize them all.…”

Section: Discussionmentioning

confidence: 99%

Algorithmic Theories of Problems. A Constructive and a Non-Constructive Approach

Pezlar

2017

LLP

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Abstract. 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 TILbased approach. The focus will be on non-empirical (i.e., mathematical and logical) problems only.

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Section: Discussionmentioning

confidence: 99%