… E(αn,βn)), where f is a connective and n is the arity of f. For every countable algebra A similar
to F and for every finite set E(p, q) of wffs in two variables we define the description of A in …

Can nonclassical logics be characterized in such a simple syn tic way? Unfortunately finding
nice refutation rules for a logic cannot be characterized by a single finite model is in most ca …

… Unfortunately, Skura’s second principle, though simpler than Goranko’s principles, is
complex enough ... Fortunately, … The completeness proof, in fact, describes a procedure …

… By the size s(F) of F we mean the number of propositional variables occurring in F. … (ii) s(F)
> 0 and this is true for normal forms of size < s(F). Then there is a literal l such that l ∨ VX ∈ Γ …

In the paper we study the method of Socratic proofs in the intuitionistic propositional logic as
a reduction procedure. Our approach consists in constructing for a given sequent α a finite …

… And we say that a normal form F is special, if the formula … We assume that Y = {F}∪U
and the rank of F is k. By using the rule HCL we reduce Y to the set Y′ = {F′,F′′}∪U (see …

Using simple algebraic methods we give Lukasiewicz-style refutation calculi for the following
intermediate logics: finite logics, LC, Yankov's logic, the logic of the weak law of excluded …

… Recently, in Skura (2019b) Skura explored the relationship between tableaux and …
logics have also been developed: In Skura (2017a) Skura used ideas from refutation systems, …

… We assume that a natural number r(F) (called the rank of F) has been assigned to every
normal form F, and some (simple) normal forms are of rank 0. … We simply say “F is …

In this paper we study the method of refutation rules in the modal logic K4. We introduce
refutation rules with certain normal forms that provide a new syntactic decision procedure for this …