| Autor: |
José Espírito Santo, Ralph Matthes, Luís Pinto |
| Jazyk: |
angličtina |
| Rok vydání: |
2013 |
| Předmět: |
|
| Zdroj: |
Electronic Proceedings in Theoretical Computer Science, Vol 126, Iss Proc. FICS 2013, Pp 28-43 (2013) |
| Druh dokumentu: |
article |
| ISSN: |
2075-2180 |
| DOI: |
10.4204/EPTCS.126.3 |
| Popis: |
We propose to study proof search from a coinductive point of view. In this paper, we consider intuitionistic logic and a focused system based on Herbelin's LJT for the implicational fragment. We introduce a variant of lambda calculus with potentially infinitely deep terms and a means of expressing alternatives for the description of the "solution spaces" (called Böhm forests), which are a representation of all (not necessarily well-founded but still locally well-formed) proofs of a given formula (more generally: of a given sequent). As main result we obtain, for each given formula, the reduction of a coinductive definition of the solution space to a effective coinductive description in a finitary term calculus with a formal greatest fixed-point operator. This reduction works in a quite direct manner for the case of Horn formulas. For the general case, the naive extension would not even be true. We need to study "co-contraction" of contexts (contraction bottom-up) for dealing with the varying contexts needed beyond the Horn fragment, and we point out the appropriate finitary calculus, where fixed-point variables are typed with sequents. Co-contraction enters the interpretation of the formal greatest fixed points - curiously in the semantic interpretation of fixed-point variables and not of the fixed-point operator. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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