11,820 research outputs found
Different Approaches to Proof Systems
The classical approach to proof complexity perceives proof systems as deterministic, uniform, surjective, polynomial-time computable functions that map strings to (propositional) tautologies. This approach has been intensively studied since the late 70’s and a lot of progress has been made. During the last years research was started investigating alternative notions of proof systems. There are interesting results stemming from dropping the uniformity requirement, allowing oracle access, using quantum computations, or employing probabilism. These lead to different notions of proof systems for which we survey recent results in this paper
Recommended from our members
Semantic memory redux: an experimental test of hierarchical category representation
Four experiments investigated the classic issue in semantic memory of whether people organize categorical information in hierarchies and use inference to retrieve information from them, as proposed by Collins & Quillian (1969). Past evidence has focused on RT to confirm sentences such as “All birds are animals” or “Canaries breathe.” However, confounding variables such as familiarity and associations between the terms have led to contradictory results. Our experiments avoided such problems by teaching subjects novel materials. Experiment 1 tested an implicit hierarchical structure in the features of a set of studied objects (e.g., all brown objects were large). Experiment 2 taught subjects nested categories of artificial bugs. In Experiment 3, subjects learned a tree structure of novel category hierarchies. In all three, the results differed from the predictions of the hierarchical inference model. In Experiment 4, subjects learned a hierarchy by means of paired associates of novel category names. Here we finally found the RT signature of hierarchical inference. We conclude that it is possible to store information in a hierarchy and retrieve it via inference, but it is difficult and avoided whenever possible. The results are more consistent with feature comparison models than hierarchical models of semantic memory
- …