Intuitionistic Hypothetical Logic of Proof
We study a term assignment for an intuitonistic fragment of the Logic of Proofs (LP). LP is a refinement of modal logic S4 in which the assertion ✷A is replaced by [[s]]A whose intended reading is “s is a proof of A”. We first introduce a natural deduction presentation based on hypothetical judgemen...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2013 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/28208 |
| Online Access: | http://hdl.handle.net/11336/28208 |
| Access Level: | Open access |
| Keyword: | Curry-Howard Logic of Proofs Lambda Calculus Programming Languages https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 |
| Summary: | We study a term assignment for an intuitonistic fragment of the Logic of Proofs (LP). LP is a refinement of modal logic S4 in which the assertion ✷A is replaced by [[s]]A whose intended reading is “s is a proof of A”. We first introduce a natural deduction presentation based on hypothetical judgements and then its term assignment, which yields a confluent and strongly normalising typed lambda calculus λIHLP. This work is part of an ongoing effort towards reformulating LP in terms of hypothetical reasoning in order to explore its applications in programming languages. |
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