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First-Order Interpolation of Non-classical Logics Derived from Propositional Interpolation

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Frontiers of Combining Systems (FroCoS 2017)

Abstract

This paper develops a general methodology to connect propositional and first-order interpolation. In fact, the existence of suitable skolemizations and of Herbrand expansions together with a propositional interpolant suffice to construct a first-order interpolant. This methodology is realized for lattice-based finitely-valued logics, the top element representing true and for (fragments of) infinitely-valued first-order Gödel logic, the logic of all linearly ordered constant domain Kripke frames.

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Acknowledgments

Partially supported by FWF P 26976, FWF I 2671 and the Czech-Austrian project MOBILITY No. 7AMB17AT054.

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Correspondence to Matthias Baaz or Anela Lolic .

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Baaz, M., Lolic, A. (2017). First-Order Interpolation of Non-classical Logics Derived from Propositional Interpolation. In: Dixon, C., Finger, M. (eds) Frontiers of Combining Systems. FroCoS 2017. Lecture Notes in Computer Science(), vol 10483. Springer, Cham. https://doi.org/10.1007/978-3-319-66167-4_15

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  • DOI: https://doi.org/10.1007/978-3-319-66167-4_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66166-7

  • Online ISBN: 978-3-319-66167-4

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