Abstract
In our previous paper [5], we have studied Kripke-type semantics for propositional logics without the contraction rule. In this paper, we will extend our argument to predicate logics without the structure rules. Similarly to the propositional case, we can not carry out Henkin's construction in the predicate case. Besides, there exists a difficulty that the rules of inference (→∀) and (∃→) are not always valid in our semantics. So, we have to introduce a notion of normal models.
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References
G. K. Dardžaniá, Intuitionsitic system without contraction, Bulletin of the Section of Logic, Polish Academy of Sciences, Institute of Philosophy and Sociology 6 (1977), pp. 2–8.
J. Ketonen and R. Weyhrauch, A decidable fragment of predicate calculus, Theoretical Computer Science 32 (1984), pp. 297–307.
Y. Komori, A new semantics for intuitionistic predicate logic, Studio Logica 45 (1986), pp. 9–17.
H. Ono, Semantical analysis of predicate logics without the contraction rule, Studia Logica 44 (1985), pp. 187–196.
H. Ono and Y. Komori, Logics without the contraction rule, Journal of Symbolic Logic 50 (1985), pp. 169–201.
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Dedicated to the memory of the late Professor Hidetosi Takahasi
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Komori, Y. Predicate logics without the structure rules. Stud Logica 45, 393–404 (1986). https://doi.org/10.1007/BF00370272
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DOI: https://doi.org/10.1007/BF00370272