74 research outputs found
Networks of Relations for Representation, Learning, and Generalization
We propose representing knowledge as a network of relations. Each relation relates only a few continuous or discrete variables, so that any overall relationship among the many variables treated by the network winds up being distributed throughout the network. Each relation encodes which combinations of values correspond to past experience for the variables related by the relation. Variables may or may not correspond to understandable aspects of the situation being modeled by the network. A distributed calculational process can be used to access the information stored in such a network, allowing the network to function as an associative memory. This process in its simplest form is purely inhibitory, narrowing down the space of possibilities as much as possible given the data to be matched. In contrast with methods that always retrieve a best fit for all variables, this method can return values for inferred variables while leaving non-inferable variables in an unknown or partially known state. In contrast with belief propagation methods, this method can be proven to converge quickly and uniformly for any network topology, allowing networks to be as interconnected as the relationships warrant, with no independence assumptions required. The generalization properties of such a memory are aligned with the network's relational representation of how the various aspects of the modeled situation are related
The Complexity of Reasoning for Fragments of Default Logic
Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified
the complexity of the extension existence problem for propositional default
logic as \SigmaPtwo-complete, and the complexity of the credulous and
skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete.
Additionally, he investigated restrictions on the default rules, i.e.,
semi-normal default rules. Selman made in 1992 a similar approach with
disjunction-free and unary default rules. In this paper we systematically
restrict the set of allowed propositional connectives. We give a complete
complexity classification for all sets of Boolean functions in the meaning of
Post's lattice for all three common decision problems for propositional default
logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-,
P-, NL-complete, trivial) for the extension existence problem, while for the
credulous and skeptical reasoning problem we obtain similar classifications
without trivial cases.Comment: Corrected versio
Effective Theories for Circuits and Automata
Abstracting an effective theory from a complicated process is central to the
study of complexity. Even when the underlying mechanisms are understood, or at
least measurable, the presence of dissipation and irreversibility in
biological, computational and social systems makes the problem harder. Here we
demonstrate the construction of effective theories in the presence of both
irreversibility and noise, in a dynamical model with underlying feedback. We
use the Krohn-Rhodes theorem to show how the composition of underlying
mechanisms can lead to innovations in the emergent effective theory. We show
how dissipation and irreversibility fundamentally limit the lifetimes of these
emergent structures, even though, on short timescales, the group properties may
be enriched compared to their noiseless counterparts.Comment: 11 pages, 9 figure
A Team Based Variant of CTL
We introduce two variants of computation tree logic CTL based on team
semantics: an asynchronous one and a synchronous one. For both variants we
investigate the computational complexity of the satisfiability as well as the
model checking problem. The satisfiability problem is shown to be
EXPTIME-complete. Here it does not matter which of the two semantics are
considered. For model checking we prove a PSPACE-completeness for the
synchronous case, and show P-completeness for the asynchronous case.
Furthermore we prove several interesting fundamental properties of both
semantics.Comment: TIME 2015 conference version, modified title and motiviatio
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