Results 21 to 30 of about 5,644 (162)
Randomisation and Derandomisation in Descriptive Complexity Theory [PDF]
Logical Methods in Computer Science, 2011 We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic L we introduce a new logic BPL, bounded error probabilistic L, which is defined from L in a similar way as the complexity class BPP ...
Kord Eickmeyer, Martin Grohe
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Journal of Logic and Computation, 2022 AbstractWe study propositional and first-order Gödel logics over infinitary languages, which are motivated semantically by corresponding interpretations into the unit interval $[0,1]$. We provide infinitary Hilbert-style calculi for the particular (propositional and first-order) cases with con-/disjunctions of countable length and prove corresponding ...
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INFINITARY LOGIC HAS NO EXPRESSIVE EFFICIENCY OVER FINITARY LOGIC
The Journal of Symbolic Logic, 2023 Abstract We can measure the complexity of a logical formula by counting the number of alternations between existential and universal quantifiers. Suppose that an elementary first-order formula $\varphi $ (in $\mathcal {L}_{\omega ,\omega }$ ) is equivalent to a formula of the infinitary ...
HARRISON-TRAINOR, MATTHEW +1 more
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On the First-Order Complexity of Induced Subgraph Isomorphism [PDF]
Logical Methods in Computer Science, 2019 Given a graph $F$, let $I(F)$ be the class of graphs containing $F$ as an induced subgraph. Let $W[F]$ denote the minimum $k$ such that $I(F)$ is definable in $k$-variable first-order logic.
Oleg Verbitsky, Maksim Zhukovskii
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On Bisimilarity for Quasi-discrete Closure Spaces [PDF]
Logical Methods in Computer ScienceClosure spaces, a generalisation of topological spaces, have shown to be a convenient theoretical framework for spatial model checking. The closure operator of closure spaces and quasi-discrete closure spaces induces a notion of neighborhood akin to that
Vincenzo Ciancia +3 more
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On the Possibility of a General Purge of Self-Reference
Análisis Filosófico, 2012 My aim in this paper is to gather some evident in favor of the view that a general purge of self-reference is possible. I do this by considering a modal-epistemic version of the Liar Paradox introduced by Roy Cook.
Lucas Rosenblatt
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A new coinductive confluence proof for infinitary lambda calculus
, 2020 We present a new and formal coinductive proof of confluence and normalisation of B\"ohm reduction in infinitary lambda calculus. The proof is simpler than previous proofs of this result.
Czajka, Łukasz
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A computability theoretic equivalent to Vaught's conjecture [PDF]
, 2013 We prove that, for every theory $T$ which is given by an ${\mathcal L}_{\omega_1,\omega}$ sentence, $T$ has less than $2^{\aleph_0}$ many countable models if and only if we have that, for every $X\in 2^\omega$ on a cone of Turing degrees, every $X ...
Montalban, Antonio
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Two complete finitary sequent calculi for reflexive common knowledge
Lietuvos Matematikos Rinkinys, 2013 This paper discusses the use of complete sequent calculi for reflexive common knowledge logic. Description of language and complete infinitary calculus for RCL is presented.
Aurimas Paulius Girčys +1 more
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Journal of the American Mathematical Society, 2012 Ordinary infinitary languages L_{lambda, kappa} satisfy the Interpolation Theorem only in the case lambda <= {aleph_1}, kappa = {aleph_0}, this include first order logic of course. There are also some pairs of such logics satifying interpolation, e.g. (L_{lambda^+,{aleph_0}}, L_{(2^lambda)^+, lambda^+}) .
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