A formal framework for specifying sequent calculus proof systems
Intuitionistic logic and intuitionistic type systems are commonly used as frameworks for the specification of natural deduction proof systems. In this paper we show how to use classical linear logic as a logical framework to specify sequent calculus proof systems and to establish some simple consequ...
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| Published in: | Theoretical computer science Vol. 474; pp. 98 - 116 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
25.02.2013
Elsevier |
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | Intuitionistic logic and intuitionistic type systems are commonly used as frameworks for the specification of natural deduction proof systems. In this paper we show how to use classical linear logic as a logical framework to specify sequent calculus proof systems and to establish some simple consequences of the specified sequent calculus proof systems. In particular, derivability of an inference rule from a set of inference rules can be decided by bounded (linear) logic programming search on the specified rules. We also present two simple and decidable conditions that guarantee that the cut rule and non-atomic initial rules can be eliminated. |
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| AbstractList | Intuitionistic logic and intuitionistic type systems are commonly used as frameworks for the specification of natural deduction proof systems. In this paper we show how to use classical linear logic as a logical framework to specify sequent calculus proof systems and to establish some simple consequences of the specified sequent calculus proof systems. In particular, derivability of an inference rule from a set of inference rules can be decided by bounded (linear) logic programming search on the specified rules. We also present two simple and decidable conditions that guarantee that the cut rule and non-atomic initial rules can be eliminated. |
| Author | Pimentel, Elaine Miller, Dale |
| Author_xml | – sequence: 1 givenname: Dale surname: Miller fullname: Miller, Dale email: dale.miller@inria.fr organization: INRIA Saclay and LIX/École Polytechnique, Palaiseau, France – sequence: 2 givenname: Elaine surname: Pimentel fullname: Pimentel, Elaine email: elaine.pimentel@gmail.com organization: Departamento de Matemáticas, Universidad del Valle, Cali, Colombia |
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| Keywords | Linear logic Cut elimination Proof systems Logical frameworks Sequent calculus |
| Language | English |
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| Title | A formal framework for specifying sequent calculus proof systems |
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