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ARXIV:2606.03655 · LOGIC AND REASONING · SUBMITTED 03 JUN · 20:49 UTC · FRESHNESS FRESH
ARXIV:2606.03655LOGIC AND REASONINGSUBMITTED 03 JUN · 20:49 UTCFRESHNESS FRESHNicholas Leisegang · Thomas Meyer · Ivan Varzniczak · arXiv
Extends propositional defeasible standpoint logic with situated conditionals to enable non-monotonic entailment checking, preserving propositional complexity bounds.
Opportunity summary
Pain Extends propositional defeasible standpoint logic with situated conditionals to enable non-monotonic entailment checking, preserving propositional complexity bounds.
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Extends propositional defeasible standpoint logic with situated conditionals to enable non-monotonic entailment checking, preserving propositional complexity bounds. applied to modal logics.
Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al. applied to modal logics.
ScienceToStartup currently rates this 0.0/10 on the public viability pass. This allows us to re-characterise the syntax of PDSL in terms of situated conditionals, and shows that a large fragment of PDSL is expressible…
Logic and Reasoning moved forward this cycle; last verified June 2026. Public score 0.0/10.
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Extends propositional defeasible standpoint logic with situated conditionals to enable non-monotonic entailment checking, preserving propositional complexity bounds.
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10.48550/arXiv.2606.03655Extends propositional defeasible standpoint logic with situated conditionals to enable non-monotonic entailment checking, preserving propositional complexity bounds.
Abstract
Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al. applied to modal logics. However, work in this field has focussed primarily on satisfiability checking, and monotonic notions of entailment, which may be inferentially weak. One particular modal logic where this has been introduced is propositional standpoint logics, where modalities can express the views of different viewpoints. This has resulted in the formalisation of propositional defeasible standpoint logic (PDSL). In this paper, we propose a means of lifting the class of (non-monotonic) rational entailment relations from traditional KLM-style reasoning to a fragment of PDSL. In order to do so, we extend the expressivity of PDSL via situated standpoint conditionals, allowing us to talk about a defeasible conditional holding in the context of a given standpoint. This allows us to re-characterise the syntax of PDSL in terms of situated conditionals, and shows that a large fragment of PDSL is expressible as a set of situated conditionals. We then focus on characterising non-monotonic entailment in this fragment, defining a method to transport any ranking-based entailment relation from the propositional case into the PDSL case. This is first described in the general case and then considered in the specific cases of rational and lexicographic closures, providing a faithful translation of each inference into PDSL. We also show that entailment-checking in this fragment of PDSL can be done largely using algorithms from the propositional case, while preserving complexity bounds.
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PROBLEM
Extends propositional defeasible standpoint logic with situated conditionals to enable non-monotonic entailment checking, preserving propositional complexity bounds. applied to modal logics.
METHOD
Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al. applied to modal logics.
RESULT
ScienceToStartup currently rates this 0.0/10 on the public viability pass. This allows us to re-characterise the syntax of PDSL in terms of situated conditionals, and shows that a large fragment of PDSL is expressible as a set of situated conditionals.
WHY NOW
Logic and Reasoning moved forward this cycle; last verified June 2026. Public score 0.0/10.
{"file name": "input.pdf", "number of pages": 18, "author": "Nicholas Leisegang; Thomas Meyer; Ivan Varzniczak", "title": "Towards Non-Monotonic Entailment in Propositional Defeasible Standpoint Logic"
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Extends propositional defeasible standpoint logic with situated conditionals to enable non-monotonic entailment checking, preserving propositional complexity bounds.
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