Algebraic proof theory for LE-logics
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2018
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| _version_ | 1866913197939752960 |
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| author | Greco, Giuseppe Jipsen, Peter Liang, Fei Palmigiano, Alessandra Tzimoulis, Apostolos |
| author_facet | Greco, Giuseppe Jipsen, Peter Liang, Fei Palmigiano, Alessandra Tzimoulis, Apostolos |
| contents | In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics). Specifically, we generalise the residuated frames in [34] to arbitrary signatures of normal lattice expansions (LE). Such a generalization provides a valuable tool for proving important properties of LE-logics in full uniformity. We prove semantic cut elimination for the display calculi D.LE associated with the basic normal LE-logics and their axiomatic extensions with analytic inductive axioms. We also prove the finite model property (FMP) for each such calculus D.LE, as well as for its extensions with analytic structural rules satisfying certain additional properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_04642 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Algebraic proof theory for LE-logics Greco, Giuseppe Jipsen, Peter Liang, Fei Palmigiano, Alessandra Tzimoulis, Apostolos Logic In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics). Specifically, we generalise the residuated frames in [34] to arbitrary signatures of normal lattice expansions (LE). Such a generalization provides a valuable tool for proving important properties of LE-logics in full uniformity. We prove semantic cut elimination for the display calculi D.LE associated with the basic normal LE-logics and their axiomatic extensions with analytic inductive axioms. We also prove the finite model property (FMP) for each such calculus D.LE, as well as for its extensions with analytic structural rules satisfying certain additional properties. |
| title | Algebraic proof theory for LE-logics |
| topic | Logic |
| url | https://arxiv.org/abs/1808.04642 |