139 problems

Prawitz's semantics concerns valid arguments in first-order intuitionistic logic: an inference rule is interpreted as logically valid when it satisfies the relevant semantic condit…

Conservativity-spectrum conjecture. In general, conservativity spectra consist precisely of $\ell$-sequences.

Solovay's conjecture. ${\bf FIM}$ has the same consistency strength as ${\bf BI}$.

Constructor-space factorization conjecture. All theorems of $L$ can be realized as actual factorizations in $\operatorname{CatTh}[E_L,\mathcal{F}]$.

The discussion concerns a family of $4$-dimensional resource-management cells arising from local computations on proofs, including cells for a weakening followed by a contraction,…

Separation conjecture. For every derivation $T\vdash_{\mathsf{SKS}}R$, there is a derivation of the form

Interpolation conjecture. For every derivation $T\vdash_{\mathsf{SKS}}R$, there is a structure $P$ and derivations

Let derivations be derivations in natural deduction, and let a derivation be reduced to a normal form by the normalization procedures of the system. Prawitz's Normalization Conject…

Let two derivations have the same premises and conclusions, and let their generality record which occurrences of variables must remain occurrences of the same variable under every…

Let derivations be derivations in a natural-deduction system, and let two derivations be equivalent when they have the same assumptions and conclusion and belong to the reflexive,…

Intuitionistic computability logic conjecture. The set of valid formulas of the resulting fragment of computability logic is described by Heyting's intuitionistic calculus…

Special-case vertical non-uniqueness conjecture. Special cases are not vertically unique.

Vertical non-uniqueness conjecture. For every connective $\texttt{\#}$, if $\texttt{\#}\in\texttt{PC}$ but $\texttt{\#}\notin\texttt{PU}$, then $\texttt{\#}$ is not vertically inte…

Counterexample-sequent conjecture. For each such connective, a suitable sequent $s$ should exist for which the required failure of vertical interderivability can be established.

The paper considers the classical positive free logic systems appearing in Theorem … are proper. (b) \mathbf{CPF}^{\begin{sideways}\begin{sideways}iota…

Let $\mathsf{LNS^{\infty}_{LTL}}$ be the non-wellfounded linear nested sequent calculus for linear temporal logic. Syntactic cut-elimination conjecture. The additional structural e…

Let a proper inception calculus denote the notion of proper inception calculus introduced in the cited work by De Domenico, and let the proper inception calculus proposed in the pr…

Let an inception calculus be a proper display calculus augmented with inception rules, and let an analytic inception rule be a rule in the subclass introduced for inception calculi…

Let $R$ be an operator-only Pure Recursive Calculus with a recursor rule of the form … The step argument $s$ is unrestricted, and an internally definable measure means a measure sa…

Pakhomov–Freund conjectures. The following two equivalences are conjectured:

Let $\operatorname{KT}_{\ell}(\omega)$ denote labelled Kruskal's theorem with labels drawn from $\omega$, and let $\operatorname{KT}_{\ell}(n)$ denote its restriction to labels bel…

Consider an inferentialist analysis of second-order arithmetic, induction principles, and the definability of concepts within a framework grounded in the structure of atomic system…

Let $\mathsf{L}$ be a system of proof rules, let $\mathbf{J}$ be a procedure on proof structures, let $\mathscr{B}$ be a base, and let $\Phi$ be a proof structure. In Prawitz's set…

The methods of Sprenger and Dam and the authors' refinement concern proof translations between cyclic and inductive systems. Applicability conjecture. Both the method of Sprenger a…

Let ${\sf WF}_{[\rightarrow]}$, ${\sf WF_{N}}_{[\rightarrow]}$, ${\sf WFC}_{[\rightarrow]}$, and ${\sf WFD}_{[\rightarrow]}$ denote the implicational fragments of the corresponding…