People often reason contrary to the prescriptions of classical logic. In this project we study cases of divergence between everyday and logical-mathematical reasoning and, challenging the canonical view, we hypothesise that they are a straightforward consequence of a tendency in human cognition to neglect empty representations (neglect-zero).
We develop logics which formally represent the neglect-zero tendency and rigorously study its impact on interpretation; explore possible conventionalizations of neglect-zero effects in specific linguistic domains; and experimentally investigate the impact of neglect-zero in ordinary reasoning and its conjectured suspension for example in the context of a mathematical proof.
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Ronald de Haan has put together a prototype for a reasoning algorithm for bilateral state-based modal logic (BSML) based on answer set programming. Here you can find a brief demonstration and some explanations, as well as a list with some possible research directions: https://github.com/rdehaan/bsml-sat/blob/main/demo.ipynb There are a lot of small and large directions for improving this reasoner, and many of them are very much suitable for a small research project or a thesis. Please feel free to get in touch with Ronald (me@ronalddehaan.eu) if you are interested in this.
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