A Logic of Inability
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917450988126208 |
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| author | Wang, Shanxia |
| author_facet | Wang, Shanxia |
| contents | Coalition Logic is primarily concerned with what coalitions can achieve, whereas what coalitions cannot achieve -- their \emph{inability} -- has received comparatively little explicit attention.
This asymmetry matters in artificial intelligence and safety-critical multi-agent systems, where one often needs to specify not merely what agents are instructed or disposed not to do, but what they are \emph{unable} to bring about.
We develop a conservative extension of Coalition Logic with an explicit inability operator, interpreted as the negation of coalition ability.
This operator is introduced as a conservative and formally tractable starting point for studying inability as a modal concept in its own right.
We prove soundness, completeness, and conservativity over standard Coalition Logic, and analyse the resulting modal behaviour: anti-monotonicity with respect to coalition inclusion, contravariance with respect to goal strength, asymmetric interaction with conjunction and disjunction, failure of superadditivity, non-equivalence with opponent ability, and the connection between grand-coalition inability and systemic impossibility.
Making this definable operator explicit reveals a systematic modal structure governing the limits of agency, and supports reasoning about constraints, negative capabilities, and impossibility in multi-agent systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27917 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Logic of Inability Wang, Shanxia Logic in Computer Science Logic Coalition Logic is primarily concerned with what coalitions can achieve, whereas what coalitions cannot achieve -- their \emph{inability} -- has received comparatively little explicit attention. This asymmetry matters in artificial intelligence and safety-critical multi-agent systems, where one often needs to specify not merely what agents are instructed or disposed not to do, but what they are \emph{unable} to bring about. We develop a conservative extension of Coalition Logic with an explicit inability operator, interpreted as the negation of coalition ability. This operator is introduced as a conservative and formally tractable starting point for studying inability as a modal concept in its own right. We prove soundness, completeness, and conservativity over standard Coalition Logic, and analyse the resulting modal behaviour: anti-monotonicity with respect to coalition inclusion, contravariance with respect to goal strength, asymmetric interaction with conjunction and disjunction, failure of superadditivity, non-equivalence with opponent ability, and the connection between grand-coalition inability and systemic impossibility. Making this definable operator explicit reveals a systematic modal structure governing the limits of agency, and supports reasoning about constraints, negative capabilities, and impossibility in multi-agent systems. |
| title | A Logic of Inability |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2604.27917 |