Metcalfe, George; Cintula, Petr; Diaconescu, Denisa
(2015).
*
Skolemization for Substructural Logics.
*
In:
Davis, Martin; Fehnker, Ansgar; McIver, Annabelle; Voronkov, Andrei
(eds.)
Logic for Programming, Artificial Intelligence, and Reasoning - Proceedings of LPAR 2015. Lecture Notes in Computer Science: Vol. 9450 (pp. 1-15).
Springer
10.1007/978-3-662-48899-7_1

The usual Skolemization procedure, which removes strong quantifiers by introducing new function symbols, is in general unsound for first-order substructural logics defined based on classes of complete residuated lattices. However, it is shown here (following similar ideas of Baaz and Iemhoff for first-order intermediate logics in [1]) that first-order substructural logics with a semantics satisfying certain witnessing conditions admit a “parallel” Skolemization procedure where a strong quantifier is removed by introducing a finite disjunction or conjunction (as appropriate) of formulas with multiple new function symbols. These logics typically lack equivalent prenex forms. Also, semantic consequence does not in general reduce to satisfiability. The Skolemization theorems presented here therefore take various forms, applying to the left or right of the consequence relation, and to all formulas or only prenex formulas.

## Item Type: |
Book Section (Book Chapter) |
---|---|

## Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |

## UniBE Contributor: |
Metcalfe, George; Cintula, Petr and Diaconescu, Denisa |

## Subjects: |
500 Science > 510 Mathematics |

## ISSN: |
0302-9743 |

## ISBN: |
978-3-662-48898-0 |

## Series: |
Lecture Notes in Computer Science |

## Publisher: |
Springer |

## Language: |
English |

## Submitter: |
George Metcalfe |

## Date Deposited: |
07 Jan 2016 15:41 |

## Last Modified: |
07 Jan 2016 15:41 |

## Publisher DOI: |
10.1007/978-3-662-48899-7_1 |

## URI: |
https://boris.unibe.ch/id/eprint/74481 |