A Dual-Threshold Probabilistic Knowing Value Logic
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914422748872704 |
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| author | Wang, Shanxia |
| author_facet | Wang, Shanxia |
| contents | We introduce a dual-threshold probabilistic knowing value logic for uncertain multi-agent settings. The framework captures within a single formalism both probabilistic-threshold attitudes toward propositions and high-confidence attitudes toward term values, thereby connecting probabilistic epistemic logic with classical knowing value logic. It is especially motivated by privacy-sensitive scenarios in which an attacker assigns high posterior probability to a candidate sensitive value without guaranteeing that it is the true one.
The main idea is to separate the threshold domains of propositional and value-oriented operators. While $K_i^θ$ ranges over the full rational threshold interval, the knowing-value operator $Kv_i^η(t)$ is restricted to $(\frac{1}{2},1]$. This high-threshold restriction has a structural effect: once $η>\frac{1}{2}$, two distinct values cannot both satisfy the threshold, so uniqueness becomes automatic. Over probabilistic models with countably additive measures, $Kv_i^η(t)$ is interpreted as non-factive high-confidence value locking.
We establish sound axiomatic systems for the framework and develop a two-layer construction based on type-space distributions and assignment-configuration mappings. This resolves the joint realization problem arising from probabilistic mass allocation and value-sensitive constraints, and yields a structured weak-completeness theorem for the high-threshold fragment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24865 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Dual-Threshold Probabilistic Knowing Value Logic Wang, Shanxia Logic in Computer Science Logic We introduce a dual-threshold probabilistic knowing value logic for uncertain multi-agent settings. The framework captures within a single formalism both probabilistic-threshold attitudes toward propositions and high-confidence attitudes toward term values, thereby connecting probabilistic epistemic logic with classical knowing value logic. It is especially motivated by privacy-sensitive scenarios in which an attacker assigns high posterior probability to a candidate sensitive value without guaranteeing that it is the true one. The main idea is to separate the threshold domains of propositional and value-oriented operators. While $K_i^θ$ ranges over the full rational threshold interval, the knowing-value operator $Kv_i^η(t)$ is restricted to $(\frac{1}{2},1]$. This high-threshold restriction has a structural effect: once $η>\frac{1}{2}$, two distinct values cannot both satisfy the threshold, so uniqueness becomes automatic. Over probabilistic models with countably additive measures, $Kv_i^η(t)$ is interpreted as non-factive high-confidence value locking. We establish sound axiomatic systems for the framework and develop a two-layer construction based on type-space distributions and assignment-configuration mappings. This resolves the joint realization problem arising from probabilistic mass allocation and value-sensitive constraints, and yields a structured weak-completeness theorem for the high-threshold fragment. |
| title | A Dual-Threshold Probabilistic Knowing Value Logic |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2603.24865 |