67,986 research outputs found
The First-Order Hypothetical Logic of Proofs
The Propositional Logic of Proofs (LP) is a modal logic in which the modality â–ˇA is revisited as [​[t]​]​A , t being an expression that bears witness to the validity of A . It enjoys arithmetical soundness and completeness, can realize all S4 theorems and is capable of reflecting its own proofs ( ⊢A implies ⊢[​[t]​]A , for some t ). A presentation of first-order LP has recently been proposed, FOLP, which enjoys arithmetical soundness and has an exact provability semantics. A key notion in this presentation is how free variables are dealt with in a formula of the form [​[t]​]​A(i) . We revisit this notion in the setting of a Natural Deduction presentation and propose a Curry–Howard correspondence for FOLP. A term assignment is provided and a proof of strong normalization is given.Fil: Steren, Gabriela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de ComputaciĂłn; ArgentinaFil: Bonelli, Eduardo Augusto. Universidad Nacional de Quilmes. Departamento de Ciencia y TecnologĂa; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentin
Simple Causes of Complexity in Hedonic Games
Hedonic games provide a natural model of coalition formation among
self-interested agents. The associated problem of finding stable outcomes in
such games has been extensively studied. In this paper, we identify simple
conditions on expressivity of hedonic games that are sufficient for the problem
of checking whether a given game admits a stable outcome to be computationally
hard. Somewhat surprisingly, these conditions are very mild and intuitive. Our
results apply to a wide range of stability concepts (core stability, individual
stability, Nash stability, etc.) and to many known formalisms for hedonic games
(additively separable games, games with W-preferences, fractional hedonic
games, etc.), and unify and extend known results for these formalisms. They
also have broader applicability: for several classes of hedonic games whose
computational complexity has not been explored in prior work, we show that our
framework immediately implies a number of hardness results for them.Comment: 7+9 pages, long version of a paper in IJCAI 201
Towards an Efficient Evaluation of General Queries
Database applications often require to
evaluate queries containing quantifiers or disjunctions,
e.g., for handling general integrity constraints. Existing
efficient methods for processing quantifiers depart from the
relational model as they rely on non-algebraic procedures.
Looking at quantified query evaluation from a new angle,
we propose an approach to process quantifiers that makes
use of relational algebra operators only. Our approach
performs in two phases. The first phase normalizes the
queries producing a canonical form. This form permits to
improve the translation into relational algebra performed
during the second phase. The improved translation relies
on a new operator - the complement-join - that generalizes
the set difference, on algebraic expressions of universal
quantifiers that avoid the expensive division operator in
many cases, and on a special processing of disjunctions by
means of constrained outer-joins. Our method achieves an
efficiency at least comparable with that of previous
proposals, better in most cases. Furthermore, it is considerably
simpler to implement as it completely relies on
relational data structures and operators
Minimization for Generalized Boolean Formulas
The minimization problem for propositional formulas is an important
optimization problem in the second level of the polynomial hierarchy. In
general, the problem is Sigma-2-complete under Turing reductions, but
restricted versions are tractable. We study the complexity of minimization for
formulas in two established frameworks for restricted propositional logic: The
Post framework allowing arbitrarily nested formulas over a set of Boolean
connectors, and the constraint setting, allowing generalizations of CNF
formulas. In the Post case, we obtain a dichotomy result: Minimization is
solvable in polynomial time or coNP-hard. This result also applies to Boolean
circuits. For CNF formulas, we obtain new minimization algorithms for a large
class of formulas, and give strong evidence that we have covered all
polynomial-time cases
Lecture notes on sediment transportation and channel stability
These notes have been prepared for a series of lectures on
sediment transportation and channel stability given by the authors to a group of engineers and geologists of the U. S. Department of Agriculture assembled at Caltech on September 12-16,1960. The material herein is not intended to serve as a complete textbook, because it covers only subjects of the one-week sequence of lectures Due to limitation of space and time, coverage of many subjects is brief and others are omitted altogether. At the end of each chapter the reader will find a selected list of references for more detailed study
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