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We show that the lattices of the normal extensions of four well-known logics—propositional intuitionistic logic $$\mathbf {Int}$$ Int , Grzegorczyk logic $$\mathbf {Grz}$$ Grz , modalized Heyting calculus $$\mathbf {mHC}$$ mHC and $$\mathbf {K4.Grz}$$ K 4 . Grz —can be joined in a commutative diagram. One connection of this diagram is an isomorphism between the lattices...
We present the logical friendliness relation in a proof-theoretic fashion as sequent system . 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 , so that the latter becomes part of the definition of system ...
We develop a multi-valued logic approach to data base design, that are tolerant to inconsistent information. Also, we discuss possible knowledge transformers in one type of such data bases.
We deal with monotone structural deductive systems in an unspecified propositional language $${\mathcal{L}}$$ L . These systems fall into several overlapping classes, forming a hierarchy. Along with well-known classes of deductive systems such as those of implicative, Fregean and equivalential systems, we consider new classes of unital and weakly implicative systems. The latter class is auxiliary,...
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