31,193 research outputs found
Strategic Argumentation is NP-Complete
In this paper we study the complexity of strategic argumentation for dialogue
games. A dialogue game is a 2-player game where the parties play arguments. We
show how to model dialogue games in a skeptical, non-monotonic formalism, and
we show that the problem of deciding what move (set of rules) to play at each
turn is an NP-complete problem
PSPACE Bounds for Rank-1 Modal Logics
For lack of general algorithmic methods that apply to wide classes of logics,
establishing a complexity bound for a given modal logic is often a laborious
task. The present work is a step towards a general theory of the complexity of
modal logics. Our main result is that all rank-1 logics enjoy a shallow model
property and thus are, under mild assumptions on the format of their
axiomatisation, in PSPACE. This leads to a unified derivation of tight
PSPACE-bounds for a number of logics including K, KD, coalition logic, graded
modal logic, majority logic, and probabilistic modal logic. Our generic
algorithm moreover finds tableau proofs that witness pleasant proof-theoretic
properties including a weak subformula property. This generality is made
possible by a coalgebraic semantics, which conveniently abstracts from the
details of a given model class and thus allows covering a broad range of logics
in a uniform way
Strong Normalization for HA + EM1 by Non-Deterministic Choice
We study the strong normalization of a new Curry-Howard correspondence for HA
+ EM1, constructive Heyting Arithmetic with the excluded middle on
Sigma01-formulas. The proof-term language of HA + EM1 consists in the lambda
calculus plus an operator ||_a which represents, from the viewpoint of
programming, an exception operator with a delimited scope, and from the
viewpoint of logic, a restricted version of the excluded middle. We give a
strong normalization proof for the system based on a technique of
"non-deterministic immersion".Comment: In Proceedings COS 2013, arXiv:1309.092
Backprop as Functor: A compositional perspective on supervised learning
A supervised learning algorithm searches over a set of functions
parametrised by a space to find the best approximation to some ideal
function . It does this by taking examples , and updating the parameter according to some rule. We define a
category where these update rules may be composed, and show that gradient
descent---with respect to a fixed step size and an error function satisfying a
certain property---defines a monoidal functor from a category of parametrised
functions to this category of update rules. This provides a structural
perspective on backpropagation, as well as a broad generalisation of neural
networks.Comment: 13 pages + 4 page appendi
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