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Register a new userReasoning about conscious experience with axiomatic and graphical mathematics
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We cast aspects of consciousness in axiomatic mathematical terms, using the graphical calculus of general process theories (a.k.a symmetric monoidal categories and Frobenius algebras therein). This calculus exploits the ontological neutrality of process theories. A toy example using the axiomatic calculus is given to show the power of this approach, recovering other aspects of conscious experience, such as external and internal subjective distinction, privacy or unreadability of personal subjective experience, and phenomenal unity, one of the main issues for scientific studies of consciousness. In fact, these features naturally arise from the compositional nature of axiomatic calculus.
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In 2006, during a meeting of a working group of scientists in La Jolla, California at The Neurosciences Institute (NSI), Gerald Edelman described a roadmap towards the creation of a Conscious Artifact. As far as I know, this roadmap was not published. However, it did shape my thinking and that of many others in the years since that meeting. This short paper, which is based on my notes taken during the meeting, describes the key steps in this roadmap. I believe it is as groundbreaking today as it was more than 15 years ago.
Quantum measurement theory is applied to quantum-like modeling of coherent generation of perceptions and emotions and generally for emotional coloring of conscious experiences. In quantum theory, a system should be separated from an observer. The brain performs self-measurements. To model them, we split the brain into two subsystems, unconsciousness and consciousness. They correspond to a system and an observer. The states of perceptions and emotions are described through the tensor product decomposition of the unconscious state space; similarly, there are two classes of observables, for conscious experiencing of perceptions and emotions, respectively. Emotional coloring is coupled to quantum contextuality: emotional observables determine contexts. Such contextualization reduces degeneration of unconscious states. The quantum-like approach should be distinguished from consideration of the genuine quantum physical processes in the brain (cf. Penrose and Hameroff). In our approach the brain is a macroscopic system which information processing can be described by the formalism of quantum theory.
Question: I have five fingers but I am not alive. What am I? Answer: a glove. Answering such a riddle-style question is a challenging cognitive process, in that it requires complex commonsense reasoning abilities, an understanding of figurative language, and counterfactual reasoning skills, which are all important abilities for advanced natural language understanding (NLU). However, there are currently no dedicated datasets aiming to test these abilities. Herein, we present RiddleSense, a new multiple-choice question answering task, which comes with the first large dataset (5.7k examples) for answering riddle-style commonsense questions. We systematically evaluate a wide range of models over the challenge, and point out that there is a large gap between the best-supervised model and human performance -- suggesting intriguing future research in the direction of higher-order commonsense reasoning and linguistic creativity towards building advanced NLU systems.
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof assistants that are based on type theory, like Coq. The reason is that it involves type definitions, such as those of type-level fixpoint operators, that are not strictly positive. The known work-around of impredicative encodings is problematic, insofar as it impedes conventional inductive reasoning. Weak induction principles can be used instead, but they considerably complicate proofs. This paper proposes a novel and simpler technique to reason inductively about impredicative encodings, based on Mendler-style induction. This technique involves dispensing with dependent induction, ensuring that datatypes can be lifted to predicates and relying on relational formulations. A case study on proving subject reduction for structural operational semantics illustrates that the approach enables modular proofs, and that these proofs are essentially similar to conventional ones.
We propose a suite of reasoning tasks on two types of relations between procedural events: goal-step relations (learn poses is a step in the larger goal of doing yoga) and step-step temporal relations (buy a yoga mat typically precedes learn poses). We introduce a dataset targeting these two relations based on wikiHow, a website of instructional how-to articles. Our human-validated test set serves as a reliable benchmark for commonsense inference, with a gap of about 10% to 20% between the performance of state-of-the-art transformer models and human performance. Our automatically-generated training set allows models to effectively transfer to out-of-domain tasks requiring knowledge of procedural events, with greatly improved performances on SWAG, Snips, and the Story Cloze Test in zero- and few-shot settings.
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