931 research outputs found
Learning the Semantics of Manipulation Action
In this paper we present a formal computational framework for modeling
manipulation actions. The introduced formalism leads to semantics of
manipulation action and has applications to both observing and understanding
human manipulation actions as well as executing them with a robotic mechanism
(e.g. a humanoid robot). It is based on a Combinatory Categorial Grammar. The
goal of the introduced framework is to: (1) represent manipulation actions with
both syntax and semantic parts, where the semantic part employs
-calculus; (2) enable a probabilistic semantic parsing schema to learn
the -calculus representation of manipulation action from an annotated
action corpus of videos; (3) use (1) and (2) to develop a system that visually
observes manipulation actions and understands their meaning while it can reason
beyond observations using propositional logic and axiom schemata. The
experiments conducted on a public available large manipulation action dataset
validate the theoretical framework and our implementation
An interpretation of the Sigma-2 fragment of classical Analysis in System T
We show that it is possible to define a realizability interpretation for the
-fragment of classical Analysis using G\"odel's System T only. This
supplements a previous result of Schwichtenberg regarding bar recursion at
types 0 and 1 by showing how to avoid using bar recursion altogether. Our
result is proved via a conservative extension of System T with an operator for
composable continuations from the theory of programming languages due to Danvy
and Filinski. The fragment of Analysis is therefore essentially constructive,
even in presence of the full Axiom of Choice schema: Weak Church's Rule holds
of it in spite of the fact that it is strong enough to refute the formal
arithmetical version of Church's Thesis
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