Abstract
The logic of partial terms (LPT) is a variety of negative free logic. In LPT, functions, as well as predicates, are strict, and free variables are given the generality interpretation. Both nonconstructive (classical) and intuitionist brands of negative free logic have served in foundational investigations, and Hilbert-style axiomatizations, natural deduction systems, and Gentzen-style sequents have been developed for them. This paper focuses on nonconstructive LPT with definite descriptions, called LPD, lays the foundation for tableaux systems by defining the concept of an LPD model system and establishing Hintikka’s Lemma, and summarizes the corresponding tableaux proof rules.
Karel Lambert helped me understand better the nature and scope of free logics. All of my previous work had been with positive free logics, and he introduced me to negative free logics. I am grateful to him for a number of useful suggestions.
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Gumb, R.D. (2000). Model Sets in a Nonconstructive Logic of Partial Terms with Definite Descriptions. In: Dyckhoff, R. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2000. Lecture Notes in Computer Science(), vol 1847. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722086_22
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DOI: https://doi.org/10.1007/10722086_22
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