9 problems

Let the logic of Section $\mathrm{logics}$ be the logic studied in the paper, and let its completeness proof be the proof given in the appendix. Consider more expressive languages…

Finite matrix nonrepresentability conjecture. The logics $Ciu^{\ast}_n$ do not admit finite matrix representations.

Modularity conjecture. The combination of these two fragments is the full classical negation–disjunction–implication fragment:

Graded–non-graded switching conjecture. If the system ${\mathrm {GRPL}}$ were developed in more detail, it would also include rules allowing switching between graded and non-graded…

The paper considers graph-based and polarity-based semantics for LE-logics, together with their many-valued generalizations, and observes that the semantic level is determined by p…

Let a consequence relation be a relation between sets of formulas that admits a collection of regular connectives, and let classical logic provide the reference collection of regul…

Generalization conjecture. The results should also generalize to mixed equilibria in infinite games by employing quantified propositional logics.

The paper considers the satisfiability problem for the many-valued modal languages and models introduced there, with finitely many possible truth values. PSPACE-hardness conjecture…

Let the truth values of Łukasiewicz logic range over the real numbers in the interval $[0,1]$, and let a certain Hilbert-style system be the system Łukasiewicz specified for this l…