Showing papers in "Annals of Pure and Applied Logic in 1994"

TL;DR: The shriek modality \s! of linear logic performs two tasks: it restores in annotated from both weakening and contraction and it separates these tasks by introducing two modalities: ! w for weakening and ! c for contraction.

TL;DR: System of axioms for a logic with operators “A is provable” and “p is a proof of A” are introduced, provided with Kripke semantics and decision procedure.

TL;DR: It is shown that the (O-minimal) theory of the ordered field of real numbers augmented by all restricted analytic functions and all real power functions admits elimination of quantifiers and has a universal axiomatization.

TL;DR: A simple method is described in order to obtain programs from proofs in second-order classical logic by extending to classical logic the results about storage operators (typed λ-terms which simulate call-by-value in call- by-name) proved by Krivine (1990) for intuitionistic logic.

TL;DR: It is shown that C-minimal fields are precisely valued algebraically closed fields, and that, if certain specific ‘bad’ functions are not definable, then algebraic closure has the exchange property, and for definable sets dimension coincides with the rank obtained from algebraicclosure.

TL;DR: This paper provides a partial solution to the completeness problem for Joyal’s axiomatization of open and etale maps, under the additional assumption that a collection axiom (related to the set-theoretical axiom with the same name) holds.

TL;DR: This paper contains proof-theoretic investigation on extensions of Kripke-Platek set theory, KP, which accommodate first-order reflection, which leads to consistency proofs for the theories KP+Пn reflection using a small amount of arithmetic (PRA) and the well-foundedness of a certain ordinal system with respect to primitive decending sequences.

TL;DR: A complete computational interpretation is given for the Horn fragment of Linear Logic and some natural generalizations of it enriched by the two additive connectives, which obtain the affirmative solution for the problem whether the multiplicative fragment of linear logic is NP-complete.

TL;DR: This work considers a scenario whereby the learner observes f and asks queries to some set A, and proves several results about when these degrees are trivial, and when the degrees are omniscient.

TL;DR: Using the concept of progress measure, a new proof is given of Rabin's fundamental result that the languages defined by tree automata are closed under complementation and an immediate determinacy property holds for the player who is trying to win according to a Rabin acceptance condition.

TL;DR: In this paper a rudimentary language of structured theory presentations is presented, and the use of this structure in proof search for an arbitrary object logic is explored.

TL;DR: This paper provides empirical support for Simpson's claim that "ATRo is the weakest set of axioms which permits the development of a decent theory of countable ordinals" and analyzes the provability of statements about countable well­ orderings within weak subsystems of second-order arithmetic.

TL;DR: This work gives a complete computational interpretation for the !-Horn fragment of Linear Logic and for some natural generalizations of it formed by introducing additive connectives, and proves that standard Minsky machines can be directly encoded in this (!, ⊕)-Horn fragments.

TL;DR: It is proved the decidability of the particular case in which the variables occuring in the problem are at most third order.

TL;DR: It is shown that a 0–1 law holds for propositional modal logic, both for structure validity and frame validity, which leads to an elegant axiomatization for almost-sure structure validity, and to sharper complexity bounds.

TL;DR: It is proved that, for any communicative associative ring R and any infinite power λ, I(λ, R) = I (λ, UTn(R)), and the number of models in a power of the theory of a unitriangular group is counted.

TL;DR: This measure is extremely complex and displays certain formally pathological features, including infinite density at all points of a certain dense subset of [0, 1].

TL;DR: The Wadge classes of a first category homogeneous zero-dimensional Borel set X can be embedded in P (ω) as an ideal on ω if and only if X is homeomorphic to X × X and X is Wadge-equivalent toX × X.

TL;DR: This paper extends Rieter's normal default theories, which have a number of the nice properties which make them a desirable context for belief revision, to the setting of nonmonotonic rule systems and extends the notion ofnormal default theories with respect to a general consistency property.

TL;DR: In this paper, the first examples of rings of algebraic numbers containing the rings of integers of the infinite algebraic extensions of Q where Hilbert's Tenth Problem is undecidable were given.

TL;DR: The polymodal provability logics for natural recursive progressions of theories based on iteration of consistency are characterized and a system of ordinal notation is constructed, which gives exactly one notation to each constructive ordinal, such that the logic corresponding to any progression along coincides with that along natural Kalmar elementary well-orderings.

TL;DR: A typing system which captures the catch/throw mechanism in the proofs-as-programs notion and can be regarded as a constructive logic with facilities for exception handling, which includes inference rules corresponding to the operations of catch and throw.

TL;DR: This paper develops a theory of “instantiate- by-need” that performs instantiations (not necessarily ground instantiations) only when needed and proves that this method is sound and complete when computing answer substitutions for non-ground logic programs including those containing function symbols.

TL;DR: It is shown that every analytic set in the Baire space which is dominating contains the branches of a uniform tree, i.e. a superperfect tree with the property that for every splitnode all the successor splitnodes have the same length, and it is proved that ∑ 1 2 - Kσ -regularity implies ∑ 2 - u - regularity.

TL;DR: A model is described where types are special subsets of a D∞ model for λ-calculus, without imposing any formal contractiveness constraint on types of the kind considered for a closely related system by MacQueen, Plotkin and Sethi (1986).

TL;DR: It is shown that there is an internal realizability definition in Eff, i.e. a syntactical translation of the internal language of Eff into itself of form “n realizes ϕ”, which extends Kleene's definition, and a certain completeness property of the (internal) category of “modest sets” can be derived in third-order arithmetic from the realizable axioms.

TL;DR: A nonstandard universe is constructed from a superstructure in a Boolean-valued model of set theory, which provides a new framework of nonstandard analysis with which methods of forcing are incorporated naturally.

TL;DR: An axiomatization and decidability of the sets of the modal formulas which are schemata of: (1) PA-provable, (2) true arithmetical sentences.

TL;DR: It is shown that, unless ω1 is an inaccessible cardinal in L, a relatively weak fragment of Martin's axiom implies that there exists a δ13 set of reals without the property of Baire.

TL;DR: Subrecursive hierarchy classifications are used to compare the complexities of recursive functions according to their derivations in a version of Kleene's equation calculus, and their computations by term-rewriting.