Löb-Safe Logics for Reflective Agents
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909293324795904 |
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| author | Ahrenbach, Seth |
| author_facet | Ahrenbach, Seth |
| contents | Epistemic and doxastic logics are modal logics for knowledge and belief, and serve as foundational models for rational agents in game theory, philosophy, and computer science. We examine the consequences of modeling agents capable of a certain sort of reflection. Such agents face a formal difficulty due to Löb's Theorem, called Löb's Obstacle in the literature. We show how the most popular axiom schemes of epistemic and doxastic logics suffer from Löb's Obstacle, and present two axiom schemes that that avoid Löb's Obstacle, which we call Reasonable Löb-Safe Epistemic Doxastic logic (${LSED}^R$) and Supported Löb-Safe Epistemic Doxastic logic (${LSED}^S$). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_09590 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Löb-Safe Logics for Reflective Agents Ahrenbach, Seth Logic in Computer Science Epistemic and doxastic logics are modal logics for knowledge and belief, and serve as foundational models for rational agents in game theory, philosophy, and computer science. We examine the consequences of modeling agents capable of a certain sort of reflection. Such agents face a formal difficulty due to Löb's Theorem, called Löb's Obstacle in the literature. We show how the most popular axiom schemes of epistemic and doxastic logics suffer from Löb's Obstacle, and present two axiom schemes that that avoid Löb's Obstacle, which we call Reasonable Löb-Safe Epistemic Doxastic logic (${LSED}^R$) and Supported Löb-Safe Epistemic Doxastic logic (${LSED}^S$). |
| title | Löb-Safe Logics for Reflective Agents |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2408.09590 |