Showing papers in "Annals of Pure and Applied Logic in 2005"

TL;DR: This semantics is used to give new proofs of several basic results concerning LP, and the realization of S4 into LP is established in a way that carefully examines and explicates the role of the + operator.

TL;DR: A natural, albeit non first-order, axiomatisation is given for the corresponding class of structures and this gives grounds to conjecture that the unique model of cardinality continuum is isomorphic to the field of complex numbers with exponentiation.

TL;DR: This paper proves both a correspondence and a canonicity result for distributive modal logics axiomatized by Sahlqvist axioms, and defines both algebraic semantics and relational semantics for these logics.

TL;DR: A new functional interpretation, based on a novel assignment of formulas, does not care for precise witnesses of existential statements, but only for bounds for them, and new principles are supported, including the FAN theorem, weak Konig's lemma and the lesser limited principle of omniscience.

TL;DR: Properties of certain directed graphs, obtained from the families of sets with special effective enumeration properties, are exploited to generalize several results in computable model theory to higher levels of the hyperarithmetical hierarchy.

TL;DR: Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic, as well as the logics of dynamic topological systems, just as S4 is the logic of topological spaces.

TL;DR: It is proved that a finitely generated group is context-free whenever its Cayley-graph has a decidable monadic second-order theory and also proves a conjecture of Schupp.

TL;DR: It is proved that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index and G/G 00 equipped with the “logic topology” is a compact Lie group.

TL;DR: It is proved that S4 is complete with respect to Boolean combinations of countable unions of convex subsets of the real line, thus strengthening a 1944 result of McKinsey and Tarski.

TL;DR: This work presents several deductive systems for common knowledge above epistemic logics –such as K, T, S4 and S5 –with a fixed number of agents and focuses on structural and proof-theoretic properties of these calculi.

TL;DR: An extension of Heyting arithmetic in finite types called Uniform Heyting Arithmetic ( HA u) is presented that allows for the extraction of optimized programs from constructive and classical proofs while keeping explicit control over the levels of recursion and the decision procedures for predicates used in the extracted program.

TL;DR: This work provides a combinatorial characterization of P -indestructibility and constructs maximal almost disjoint families which are P - indestructible yet Q -destructible for several pairs of forcing notions ( P, Q ) .

TL;DR: A weak system of intuitionistic second-order arithmetic, WKV, a subsystem of the one in S.C. Kleene, R.E. Vesley, is presented, it is shown that some statements of real analysis, like a version of the Heine–Borel Theorem, and some statement of logic, e.g. compactness of classical proposition calculus, are equivalent to the (Weak) Fan Theorem in this system.

TL;DR: Using a versatile and flexible compression technique, regularity properties of ordinal count functions can be used to prove logical limit laws.

TL;DR: Every stable theory that is interpretable in a geometric surgical theory is superstable of finite U -rank, which means that every stable theory in the class of geometric surgical theories is superstably interpretable.

TL;DR: It is proved that intuitionistic logic can be replaced with any other proper intermediate logic without modifying the resulting semantics, and it is shown that the answer set semantics satisfies an important property, the “extension by definition”, that can be used to construct program translations.

TL;DR: In this article, a Kripke model of CZF is presented in which Power Set is false and Subset Collection is replaced by Exponentiation, in which Subset collection fails.

TL;DR: This work captures the principal models of computation and specification in the literature by a uniform set of transparent mathematical descriptions which—starting from scratch—provide the conceptual basis for a comparative study.

TL;DR: A system of simply typed lambda terms (with fixed point combinators) is introduced and it is shown that a rather comprehensive class of (co-)recursion equations on streams or non-wellfounded trees can be solved in this system.

TL;DR: This work proves a full completeness theorem for multiplicative–additive linear logic using a double gluing construction applied to Ehrhard’s *-autonomous category of hypercoherences, and guarantees that every dinatural transformation corresponds to a Girard MALL proof-structure.

TL;DR: This first paper on constructive concurrent dynamic logic (CCDL) gives a satisfactory treatment of what statements are forced to be true by partial information about the underlying computer, and develops a constructive logic programming tool for specification and modular verification of programs in any imperative concurrent language.

TL;DR: A new proof of the completeness of the modal logic S 4 for all topological spaces as well as for the real line R, the n -dimensional Euclidean space R n and the segment (0, 1) etc is presented.

TL;DR: It is shown that the converse is not true, and any function that is computable in the sense of Markov, i.e., computable with respect to a standard Godel numbering of the computable real numbers, is computability in thesense of Banach and Mazur.

TL;DR: It is shown that Greibach’s normal form theorem depends only on a few equational properties of least pre-fixed points in semirings, and eliminations of chain and deletion rules depend on their inequational properties (and the idempotence of addition).

TL;DR: It is proved that a quantifier elimination result for existentially closed n -truncated Hasse fields is proved and the fields are characterized as reducts of existenceentially closed Hasse Fields.

TL;DR: An approach based on reducibility candidates is presented that uses non-strictly positive inductive definitions and covers second-order universal quantification and also the extension of the logic with fixed points of non-Strictly negative operators, which appears to be a new result.

TL;DR: The properties of focalization and reversion of linear proofs are at the heart of the analysis: it is shown that the tq-protocol of normalization for the classical systems LK pol η and LK Pol η , ρ perfectly fits normalization of polarized proof-nets.

TL;DR: A certain class of pretoposes are constructed, consisting of what one might call “predicative realizability toposes”, that can act as categorical models of certain predicative type theories, including Martin-Lof Type Theory.

TL;DR: This paper proves exponential separations between depth d-LK and depth (d + 1 )-K for every d 2 1 N utilizing the order induction principle, and deduces width lower bounds for resolution refutations of the Ramsey principle.

TL;DR: A categorical model of polymorphism, based on game semantics, which contains a large collection of generic types and solves a recursive equation involving this relative product to obtain a universe in a suitably “absolute” sense.