Negative Modal Operators in Intuitionistic Logic
Negative modal operators in intuitionistic logic.
Normal forms in partial modal logic
A "partial" generalization of Fine's definition [Fin] of normal forms in normal minimal modal logic is given. This means quick access to complete axiomatizations and decidability proofs for partial modal logic [Thi].
O dynamické logice
On Core XPath with Inflationary Fixed Points
We prove the undecidability of Core XPath 1.0 (CXP) [G. Gottlob and C. Koch, in Proc. of 17th Ann. IEEE Symp. on Logic in Computer Science, LICS ’02 (Copenhagen, July 2002). IEEE CS Press (2002) 189–202.] extended with an Inflationary Fixed Point (IFP) operator. More specifically, we prove that the satisfiability problem of this language is undecidable. In fact, the fragment of CXP+IFP containing only the self and descendant axes is already undecidable.
On interpretability in theories containing arithmetic. II.
On Intuitionistic Sentential Connectives I.
On Lamport's comparison between linear and branching time temporal logic
On some properties of grounding nonuniform sets of modal conjunctions
A language grounding problem is considered for nonuniform sets of modal conjunctions consisting of conjunctions extended with more than one modal operator of knowledge, belief or possibility. The grounding is considered in the context of semiotic triangles built from language symbols, communicative cognitive agents and external objects. The communicative cognitive agents are assumed to be able to observe external worlds and store the results of observations in internal knowledge bases. It is assumed...
On the geometry of intuitionistic S4 proofs.
On the relation of three-valued logic to modal logic
On the representation of S5 algebras and their automorphism groups.
Polyadic algebras over nonclassical logics
The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)'s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.
Positive Logic with Double Negation
Positive logic with double negation.
Preservation of admissibility of inference rules in the logics similar to S4. 2.
Propositional dynamic logic with recursive programs
Provability in arithmetic and a schema of Grzegorczyk
Remarks on intuitionistic modal logics.
Representing Upper Probability Measures over Rational Lukasiewicz Logic.