Abstract
We present the logical friendliness relation in a proof-theoretic fashion as sequent system \(\boldsymbol{F}\). Then, the completeness theorem is proved. On the way to this theorem, we characterize the notion of satisfiability with respect to the classical two-valued semantics, in a proof-theoretic manner as system \(\boldsymbol{S}\), so that the latter becomes part of the definition of system \(\boldsymbol{F}\). Also, we obtain the strong compactness property for friendliness as a corollary of our completeness theorem.
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Muravitsky, A.Y. (2009). Satisfaction and Friendliness Relations within Classical Logic: Proof-Theoretic Approach. In: Bosch, P., Gabelaia, D., Lang, J. (eds) Logic, Language, and Computation. TbiLLC 2007. Lecture Notes in Computer Science(), vol 5422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00665-4_15
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DOI: https://doi.org/10.1007/978-3-642-00665-4_15
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