Showing papers in "Annals of Pure and Applied Logic in 2022"

TL;DR: In this article , the synthetic inference rules that arise when using theories composed of bipolars have been examined in both classical and intuitionistic logics, and they have been applied to organize the proof theory of labeled sequent systems for several propositional modal logics.

TL;DR: In this paper, the authors study Kim-independence over arbitrary sets, assuming that forking satisfies existence, and establish Kim's lemma for Kim-dividing over arbitrarily sets in an NSOP1 theory.

TL;DR: In this paper , the authors consider an extension of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals and obtain sharp results on the proof-theoretic strength of these systems using methods of provability logic.

TL;DR: In this article , Kim's lemma for Kim-dividing over arbitrary sets in an NSOP 1 theory was studied and the symmetry of Kim-independence and the independence theorem for Lascar strong types was proved.

TL;DR: The semantics of non-classical logic, intuitionistic, many-valued, and quantum logic are unified by the concept of L -algebra as mentioned in this paper and three classes of algebras are associated to specializations of a bounded L-algebra, given by simple equations.

TL;DR: An expansion of Belnap–Dunn logic with belief and plausibility functions that allow non-trivial reasoning with inconsistent and incomplete probabilistic information is designed and proves completeness for both kinds of calculi and shows their equivalence by establishing faithful translations in both directions.

TL;DR: In this article , the authors show that an X-expansion of an ordered divisible abelian group always contains an o-minimal expansion of the ordered group such that all bounded X-definable sets are definable in the structure.

TL;DR: In this paper , an algebraic characterization of the notion of generalized existential completion of a conjunctive doctrine P for a class Λ of morphisms of the base category of P is provided.

TL;DR: The notion of first-order part of a computational problem was introduced by Dzhafarov, Solomon, and Yokoyama as discussed by the authors , which captures the strongest computational problem with codomain N that is Weihrauch reducible to f .

TL;DR: In this paper , it was shown that Σ11-CA is equivalent to a nonstandard model of ZFC with the axiom of choice for any cardinality α ∈OrdM, where X is the family of LM-definable subsets of M.

TL;DR: In this paper , the spectrum of independence of arbitrary cardinality ℵω has been studied and a forcing notion has been developed, which allows to join a maximal independent family with arbitrary cardinalities.

TL;DR: In this paper , a new characterization of the ideal J [ κ ] , from which it is shown that κ -Souslin trees exist in various models of interest.

TL;DR: In this paper, the authors introduce infinitary action logic with exponentiation, which is an extension of the multiplicative-additive Lambek calculus with Kleene star and a family of subexponential modalities.

TL;DR: The splitting number of the reals as discussed by the authors is a cardinal characteristic of the Hausdorff space which is connected to Efimov's problem, which asks whether every infinite compact space must contain either a non-trivial convergent sequence, or a copy of βN.

TL;DR: In this article , a modal predicate logic where names can be non-rigid and the existence of agents can be uncertain is introduced, which can handle various de dicto/de re distinctions in a natural way.

TL;DR: In this paper , the Presburger fragment of multiteam semantics is studied and it is shown that this fragment corresponds to inclusion-exclusion logic in multiteams, but, in contrast to the situation in team semantics, that it is strictly contained in independence logic.

TL;DR: In this paper , the authors studied the model theory of the ring of adeles A K of a number field K , and gave a description of the definable subsets of A K n , for any n ≥ 1 , and proved that they are measurable.

TL;DR: In this article , the authors introduce infinitary action logic with exponentiation, which is an extension of the multiplicative-additive Lambek calculus with Kleene star and a family of subexponential modalities.

TL;DR: In this article , the causal-observational languages considered in [2] can be embedded into first-order dependence logic by means of a translation and a careful choice of models, which can be refined to an embedding into the Bernays-Schönfinkel-Ramsey fragment of dependence logic or, in the restricted case of recursive causal models, into the existential fragment.

TL;DR: In this article , the authors study frame definability in finitely valued modal logics and establish two main results via suitable translations: (1) one cannot define more classes of frames than are already definable in classical modal logic (cf.

TL;DR: The splitting number of the reals as mentioned in this paper is a cardinal characteristic of the Hausdorff space, and it is connected to Efimov's problem, which asks whether every infinite compact space must contain either a non-trivial convergent sequence, or a copy of β N.

TL;DR: For every set of ordinals A in a Magidor-Radin generic extension using a coherent sequence such that oU→(κ)<κ+, there is C′⊆CG such that V[A]=V[C′] as discussed by the authors .

TL;DR: In this paper , it was shown that the First-Order Reflection Principle is not provable in KMU with global choice, but it is mutually interpretable with KMU + Limitation of Size.

TL;DR: In this article , the Ax-Schanuel inequality for the exponential differential equation and its analogue for the differential equation of the j -function are defined as predimensions and the connection of this problem to definability of derivations in the reducts of differentially closed fields is discussed.

TL;DR: In this article , an alternative interpretation of propositional inquisitive logic as an epistemic logic of knowing how is presented, in which an propositional logic formula being supported by a state is formalized as "knowing how to resolve $\alpha$" (more colloquially, "how ''alpha$ is true") holds on the S5 epistemic model corresponding to the state.

TL;DR: In this article, a new characterization of the ideal J [ κ ], from which it is shown that κ-Souslin trees exist in various models of interest.

TL;DR: In this article , the authors study hidden-variable models from quantum mechanics and their abstractions in purely probabilistic and relational frameworks by means of logics of dependence and independence, which are based on team semantics.

TL;DR: In this article , the authors study the model theory of vector spaces with a bilinear form over a fixed field, and show that linear independence forms a simple unstable independence relation.

TL;DR: In this paper , the authors provide a Gentzen-style proof theory for admissibility for six interesting intuitionistic modal logics: iCK4, iCS4≡IPC, strong Löb logic iSL, modalized Heyting calculus mHC, Kuznetsov-Muravitsky logic KM, and propositional lax logic PLL.

TL;DR: For every pair χ <κ of regular uncountable cardinals, □(κ) implies Pr1(κ,κ, ε, δ, ϵ, π, γ, ρ, σ, ω, φ, χ, ψ, υ, τ, ό, ώ, ϐ, ϒ, Ϡ, ϓ, ϖ, Ϟ, ϩ, ϑ, ϳ,ρ,φ,χ,υ,π,σ,ώ,ω,ψ,Ϡ,ό,ϐ,Ϟ,ϩ,ϵ,ϒ,ϓ,ϕ,ϔ,ϖ,τ,ϑ,ϙ,ϊ,ϳ,↵) as mentioned in this paper , where ρ is the cardinal number of the cardinal π.