Abstract
Classical propositional logic plays a prominent role in industrial applications, and yet the complexity of this logic is presumed to be non-feasible. Tractable systems such as depth-bounded boolean logics approximate classical logic and can be seen as a model for resource-bounded agents whose reasoning style is nonetheless classical. In this paper we first study a hierarchy of tractable logics that is not defined by depth. Then we extend it into a modal logic where modalities make explicit the assumptions discharged in propositional proofs, thereby expressing blueprints for proofs. A natural deduction system is provided that permits to reason about and manage such proof blueprints.
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31 July 2022
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25 May 2022
A Correction to this paper has been published: https://doi.org/10.1007/s11225-022-10006-5
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Acknowledgements
The author wishes to thank the anonymous referees for their many interesting comments and corrections. This research was funded by the Department of Philosophy “Piero Martinetti” of the University of Milan under the project “Departments of Excellence 2018-2022” awarded by the Ministry of Education, University and Research (MIUR).
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Presented by Jacek Malinowski.
The original online version of this article was revised: Footnote 1 was incorrectly published as “Or at least as the conditional in all antecedent and consequent parts, if something like Pizzi’s weak Boethius’ Thesis, \((A\rightarrow B)\supset \sim \! (A\rightarrow \sim \! B)\), is accepted as a connexive principle”, the correct footnote is. It is corrected as “Classical and epistemic logics suffer from logical omniscience problems as models of reasoning agents [46]. Epistemic logic [44] is thus said to model what an agent can know, or does implicitly know, by purely deductive methods”.
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Pardo, P. A Modal View on Resource-Bounded Propositional Logics. Stud Logica 110, 1035–1080 (2022). https://doi.org/10.1007/s11225-022-09984-3
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DOI: https://doi.org/10.1007/s11225-022-09984-3