769 research outputs found
Complexity Results for Modal Dependence Logic
Modal dependence logic was introduced recently by V\"a\"an\"anen. It enhances
the basic modal language by an operator =(). For propositional variables
p_1,...,p_n, =(p_1,...,p_(n-1);p_n) intuitively states that the value of p_n is
determined by those of p_1,...,p_(n-1). Sevenster (J. Logic and Computation,
2009) showed that satisfiability for modal dependence logic is complete for
nondeterministic exponential time. In this paper we consider fragments of modal
dependence logic obtained by restricting the set of allowed propositional
connectives. We show that satisfibility for poor man's dependence logic, the
language consisting of formulas built from literals and dependence atoms using
conjunction, necessity and possibility (i.e., disallowing disjunction), remains
NEXPTIME-complete. If we only allow monotone formulas (without negation, but
with disjunction), the complexity drops to PSPACE-completeness. We also extend
V\"a\"an\"anen's language by allowing classical disjunction besides dependence
disjunction and show that the satisfiability problem remains NEXPTIME-complete.
If we then disallow both negation and dependence disjunction, satistiability is
complete for the second level of the polynomial hierarchy. In this way we
completely classify the computational complexity of the satisfiability problem
for all restrictions of propositional and dependence operators considered by
V\"a\"an\"anen and Sevenster.Comment: 22 pages, full version of CSL 2010 pape
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
Dependence Logic with Generalized Quantifiers: Axiomatizations
We prove two completeness results, one for the extension of dependence logic
by a monotone generalized quantifier Q with weak interpretation, weak in the
meaning that the interpretation of Q varies with the structures. The second
result considers the extension of dependence logic where Q is interpreted as
"there exists uncountable many." Both of the axiomatizations are shown to be
sound and complete for FO(Q) consequences.Comment: 17 page
A logic road from special relativity to general relativity
We present a streamlined axiom system of special relativity in first-order
logic. From this axiom system we "derive" an axiom system of general relativity
in two natural steps. We will also see how the axioms of special relativity
transform into those of general relativity. This way we hope to make general
relativity more accessible for the non-specialist
Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism
This essay examines the philosophical significance of -logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of -logical validity can then be countenanced within a coalgebraic logic, and -logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of -logical validity correspond to those of second-order logical consequence, -logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets
On the Formal Semantics of IF-Like Logics
In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Information Friendly (IF) logics. In this paper we argue that this is not an inherent characteristic of these logics but a defect in the way in which the compositional semantics given by Hodges for the regular fragment was generalized to arbitrary formulas. We fix this by proposing an alternative formalization, based on a variation of the classical notion of valuation. Basic metatheoretical results are proven. We present these results for Hodges' slash logic (from which these can be easily transferred to other IF-like logics) and we also consider the flattening operator, for which we give novel game-theoretical semantics
Sahlqvist's theorem for boolean algebras with operators with an application to cylindric algebras
Evidence for protein-mediated fatty acid efflux by adipocytes
Abstract Aim: The hormonally controlled mobilization and release of fatty acids from adipocytes into the circulation is an important physiological process required for energy homeostasis. While uptake of fatty acids by adipocytes has been suggested to be predominantly protein-mediated, it is unclear whether the efflux of fatty acids also requires membrane proteins. Methods: We used fluorescent fatty acid efflux assays and colorimetric assays for free fatty acids and glycerol to identify inhibitors with effects on fatty acid efflux, but not lipolysis, in 3T3-L1 adipocytes. We assessed the effect of these inhibitors on a fibroblast-based cell line expressing fatty acid transport protein 1, hormone-sensitive lipase and perilipin, which presumably lacks adipocyte-specific proteins for fatty acid efflux. Results: We identified 4,4¢-diisothiocyanatostilbene-2,2¢-disulfonic acid (DIDS) as an inhibitor of fatty acid efflux that did not impair lipolysis or the cellular exit of glycerol but lead to an accumulation of intracellular fatty acids. In contrast, fatty acid efflux by the reconstituted cellular model for fatty acid efflux was responsive to lipolytic stimuli, but insensitive to DIDS inhibition. Conclusion: We propose that adipocytes specifically express an as yet unidentified DIDS-sensitive protein that enhances the efflux of fatty acids and therefore may lead to novel treatment approaches for obesity-related disorders characterized by abnormal lipid fluxes and ectopic triglyceride accumulation
Transformations in the law concerning slavery: legacies of the nineteenth century anti-slavery movement
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