Affiliation:
1. Università degli Studi di Siena, Siena, Italy
Abstract
We introduce a proof system for Hájek's logic
BL
based on a relational hypersequents framework. We prove that the rules of our logical calculus, called
RHBL
, are sound and invertible with respect to any valuation of
BL
into a suitable algebra, called (ω)[0,1]. Refining the notion of reduction tree that arises naturally from
RHBL
, we obtain a decision algorithm for
BL
provability whose running time upper bound is 2
O
(
n
)
, where
n
is the number of connectives of the input formula. Moreover, if a formula is unprovable, we exploit the constructiveness of a polynomial time algorithm for leaves validity for providing a procedure to build countermodels in (ω)[0, 1]. Finally, since the size of the reduction tree branches is
O
(
n
3
), we can describe a polynomial time verification algorithm for
BL
unprovability.
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
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