Showing papers in "Annals of Pure and Applied Logic in 2014"

TL;DR: It is shown that according to the simpler one, R → ¬ (the intensional fragment of R) is the minimal relevance logic, but R itself is not, while all fragments of linear logic are not.

TL;DR: In this paper, a systematic study of the class of theories without the tree property of the second kind (NTP2) was initiated, and it was shown that the burden is sub-multiplicative in NTP2 theories.

TL;DR: In this article, a category-theoretic framework for universal homogeneous objects is developed, with some applications in the theory of Banach spaces, linear orderings, and in the topology of compact Hausdorff spaces.

TL;DR: This logic makes use of a number of evidence-related notions such as availability, admissibility, and “goodness” of a piece of evidence, and is based on an innovative modification of the Fitting semantics for Artemovʼs Justification Logic designed to preempt Gettier-type counterexamples.

TL;DR: In this article, an evidence logic for epistemic agents faced with possibly contradictory evidence from different sources is developed, which is based on a neighborhood semantics, where a neighborhood N indicates that the agent has reason to believe that the true state of the world lies in N. The logic is defined in terms of this evidence structure, yielding their intended models for evidence-based beliefs.

TL;DR: It is shown that quantum B-algebras provide a unified semantic for non-commutative algebraic logic, and they cover the vast majority of implicational algebrAs like BCK-algebra, residuated lattices, partially ordered groups, BL- and MV-alGEbras, effect algeBRas, and their non-Commutative extensions.

TL;DR: A variant of Artemov’s Justification Logic in which one can say “I have degree r of confidence that t is evidence for the truth of formula F” is proposed and it is proved the usual soundness and completeness theorems.

TL;DR: It is shown that from proofs using only a limited amount of the law-of-excluded-middle, one can extract functionals, where L is a learning procedure for a rate of convergence which succeeds after at most B -many mind changes.

TL;DR: In this article, an arithmetically complete calculus with modalities labeled by natural numbers and ω, where ω corresponds to the full uniform reflection schema, whereas n ω correspond to its restriction to arithmically Π n + 1 -formulas, is presented.

TL;DR: An axiomatization of the class ECF of exponentially closed fields, which includes the pseudo-exponential fields previously introduced by the second author, is given, and it is shown that it is superstable over its interpretation of arithmetic.

TL;DR: For G a group denable in some structure M, notions of \denable" compactication of G and action of G on a compact space X are derived.

TL;DR: Some algebraic properties of partially ordered sets that depend on classes of graphs under consideration are investigated, and it is shown that some of these partial ordered sets possess atoms, minimal and maximal elements.

TL;DR: A combinatorial characterization of Martinʼs number is given for these forcing notions and a general scheme for analyzing preservation properties for them is presented.

TL;DR: This work determines the dimension spectra of a wide class of randomly selected subfractals of a given self-similar fractal and shows that each such fractal has a dimension spectrum that is a closed interval whose endpoints can be computed or approximated from the parameters of the fractal.

TL;DR: An infinitary logic for metric structures which is analogous to L ω 1 , ω is described and it is shown that this logic is capable of expressing several concepts from analysis that cannot be expressed in finitary continuous logic.

TL;DR: In this article, a class of [ 0, 1 ] -valued logics is studied and a maximality theorem characterizes these logics in terms of a model-theoretic property, namely, an extension of the omitting types theorem to uncountable languages.

TL;DR: This paper provides a possible-world semantics for FOLP, based on the propositional semantics of Fitting (2005) [5] and gives an Mkrtychev semantics.

TL;DR: The results, in combination with existing research, essentially complete the classification up to primitive recursive equivalence of those extensions of system T used to give a direct computational interpretation to choice principles.

TL;DR: In this paper, the authors investigated the relationship between the bounding number, the closed almost disjointness number, and the splitting number, as well as the existence of splitting families.

TL;DR: It is shown that every sequence admits a cohesive set (infinite rainbow) of non-PA Turing degree; and that every ∅ ′ -recursive sequence (2-bounded coloring of pairs) admits a low 3 cohesiveSet (Infinite rainbow).

TL;DR: In this paper, a semantic and algorithmic method for establishing a variant of the analytic subformula property (called the bounded proof property, bpp) for modal propositional logics is introduced.

TL;DR: It is shown that if G is any n-generic with n ≥ 2 then it satisfies the jump property G ( n − 1 ) ≡ T G ′ ⊕ ∅ ( n ) , and so cannot have even Cohen 1-generic degree.

TL;DR: This work uses square sequences to construct covering matrices for which CP and S fail, leading naturally to an investigation of square principles intermediate between □ κ and □ ( κ + ) for a regular cardinal κ.

TL;DR: In this paper, the authors introduce Basic Intuitionistic Set Theory BIST, and investigate it as a first-order set theory extending the internal logic of elementary toposes, together with the extra structure of a directed structural system of inclusions (dssi) on the topos.

TL;DR: This work provides a quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness, and provides a test for the logical omniscience problem in a given formal theory of knowledge.

TL;DR: The method of ordinal analysis developed for Kripke–Platek set theory is relativized to theories which have the power set axiom and it is shown that whenever KP(P)+AC proves a Π2P statement then it holds true in the segment Vτ of the von Neumann hierarchy.

TL;DR: The inner models with representatives in all equivalence classes of thin equivalence relations in a given projective pointclass of even level assuming projective determinacy are described and are characterized by their correctness and the property that they correctly compute the tree from the appropriate scale.

TL;DR: The preservation of selective covering properties, including classic ones introduced by Menger, Hurewicz, Rothberger, Gerlits and Nagy, and others, under products with some major families of concentrated sets of reals is studied.

TL;DR: It is shown that the separative quotient of the poset P ( L ) , ⊂ 〉 of isomorphic suborders of a countable scattered linear order L is σ -closed and atomless and all these posets are forcing-equivalent.

TL;DR: General results on extensions of models and sets of formulas are established to provide a basis for the admissible rules of the Gabbay–de Jongh logics and to show that these logics have finitary unification type.