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On complexity of propositional logics. (Russian) Zbl 0615.03023
Complexity problems of mathematical logic, Collect. sci. Works, Kalinin 1985, 80-90 (1985).
[For the entire collection see Zbl 0596.00004.]
This paper enlarges and continues an earlier one of the same author [”Polynomial finite approximability of modal and superintuitionistic logics” (Russian), Mat. Logika, Mat. Ling., Teor. Algor., Kalinin. Gos. Univ., Kalinin, 75-83 (1983)]. Taking as complexity function of a logic L the function $$f_ L:\omega \to \omega$$ with $$f_ L(n)$$ the minimal cardinality of countermodels for all non-theorems of L of length $$\leq n$$, it is shown in a first part that some intermediate logics and also some modal logics may have rapidly growing complexity functions. In a second part, the NP- reps. PSPACE-completeness of the satisfiability problem is proved for some intermediate logics.
Reviewer: S. D. Latow

##### MSC:
 03D15 Complexity of computation (including implicit computational complexity) 03B55 Intermediate logics 03B45 Modal logic (including the logic of norms)