Authors
Nils Kürbis
University of Lodz
Abstract
This paper formulates a bilateral account of harmony, which is an alternative to the one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by Kürbis and the observation that reading some of the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. Thus the consequences of asserting a formula give grounds for denying it, namely if the opposite speech act is applied to the consequences. Similarly, the consequences of denying a formula give grounds for asserting the formula. I formulate a process of inversion, which allows the determination of assertive elimination rules from assertive introduction rules, and rejective elimination rules from rejective introduction rules, and conversely. It corresponds to Francez's notion of vertical harmony. I also formulate a process of conversion, which allows the determination of rejective introduction rules from certain assertive elimination rules and conversely, and the determination for assertive introduction rules from certain rejective elimination rules and conversely. It corresponds to Francez's notion of horizontal harmony.
Keywords Logic  Denial  Harmony  Proof-theory  Negation
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References found in this work BETA

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
Proof and Falsity: A Logical Investigation.Nils Kürbis - 2019 - Cambridge, UK: Cambridge University Press.
General-Elimination Harmony and the Meaning of the Logical Constants.Stephen Read - 2010 - Journal of Philosophical Logic 39 (5):557-576.

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