The logic of equilibrium and abelian lattice order

Authors: Adriana Galli Renato A Lewin Marta Sagastume

Publish Date: 2004/01/15

Volume: 43, Issue: 2, Pages: 141-158

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Abstract

We introduce a deductive system Bal which models the logic of balance of opposing forces or of balance between conflicting evidence or influences ‘‘Truth values’’ are interpreted as deviations from a state of equilibrium so in this sense the theorems of Bal are to be interpreted as balanced statements for which reason there is only one distinguished truth value namely the one that represents equilibrium The main results are that the system Bal is algebraizable in the sense of 5 and its equivalent algebraic semantics BAL is definitionally equivalent to the variety of abelian lattice ordered groups that is the categories of the algebras in BAL and of ℓ–groups are isomorphic see 10 Ch4 4 We also prove the deduction theorem for Bal and we study different kinds of semantic consequence associated to Bal Finally we prove the coNPcompleteness of the tautology problem of Bal

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