First steps towards probabilistic justification logic

Kokkinis, Ioannis; Maksimovic, Petar; Ognjanović, Zoran; Studer, Thomas

doi:10.1093/jigpal/jzv025

Cited by 31 publications

(40 citation statements)

References 13 publications

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“…Semantics for probabilistic logics over classical propositional logic has been given both for σ-and for finitely additive measures [28]. Semantics for probabilistic logics over justification logic [18,19] has been given only for finitely additive measures. However, after the small model theorems that we will prove, the probability spaces in the models will be finite, so the results of this paper hold for the finitely additive case too.…”

Section: Preliminariesmentioning

confidence: 99%

The complexity of satisfiability in non-iterated and iterated probabilistic logics

Kokkinis

2018

Ann Math Artif Intell

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Let L be some extension of classical propositional logic. The noniterated probabilistic logic over L is the logic PL that is defined by adding non-nested probabilistic operators in the language of L. For example, in PL we can express a statement like "the probability of truthfulness of A is at least 0.3" where A is a formula of L. The iterated probabilistic logic over L is the logic PPL, where the probabilistic operators may be iterated (nested). For example, in PPL we can express a statement like "this coin is counterfeit with probability 0.6". In this paper we investigate the influence of probabilistic operators in the complexity of satisfiability in PL and PPL. We obtain complexity bounds, for the aforementioned satisfiability problem, which are parameterized in the complexity of satisfiability of conjunctions of positive and negative formulas that have neither a probabilistic nor a classical operator as a top-connective. As an application of our results we obtain tight complexity bounds for the satisfiability problem in PL and PPL when L is classical propositional logic or justification logic. keywords: probabilistic logic, computational complexity, satisfiability, justification logicAcknowledgements. The author is grateful to Antonis Achilleos and Thomas Studer for several useful discussions and suggestions and to the anonymous reviewers for many valuable comments and remarks that helped him improve the quality of this paper substantially.

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Section: Preliminariesmentioning

confidence: 99%

The complexity of satisfiability in non-iterated and iterated probabilistic logics

Kokkinis

2018

Ann Math Artif Intell

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“…Uncertain reasoning in justification logic has also been studied in [21,12,11]. See [15,16] for an extended comparison between our approach and the ones from [21,12,11].…”

Section: Introductionmentioning

confidence: 98%

“…This differentiation in credulity cannot be expressed in classical justification logic. So, the main contribution of justification logics with probability operators (probabilistic justification logics [15,16]) is the ability to compare different sources of information. Uncertain reasoning in justification logic has also been studied in [21,12,11].…”

Section: Introductionmentioning

confidence: 99%

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The Complexity of Non-Iterated Probabilistic Justification Logic

Kokkinis

2016

Lecture Notes in Computer Science

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The logic PJ is a probabilistic logic defined by adding (non-iterated) probability operators to the basic justification logic J. In this paper we establish upper and lower bounds for the complexity of the derivability problem in the logic PJ. The main result of the paper is that the complexity of the derivability problem in PJ remains the same as the complexity of the derivability problem in the underlying logic J, which is Π p 2 -complete. This implies hat the probability operators do not increase the complexity of the logic, although they arguably enrich the expressiveness of the language.1 J stands for justification, whereas PJ stands for probabilistic justification. 2 the two P's stand for iterations of the probability operator.

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“…Later, Fitting [11] introduced epistemic models for justification logic. This general reading of justification led to a big variety of epistemic justification logics for many different applications [2,3,4,6,13,14,19,20]. Instead of an implicit statement Kϕ, which stands for the agent knows ϕ, justification logics include explicit statements of the form [t]ϕ, which mean t justifies the agent's knowledge of ϕ.…”

Section: Introductionmentioning

confidence: 99%

Temporal Justification Logic

Bucheli¹,

Ghari

Studer

2017

Electron. Proc. Theor. Comput. Sci.

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Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal logics. The behavior and interaction of agents in distributed system is often modeled using logics of knowledge and time. In this paper, we sketch some preliminary ideas on how the modal knowledge part of such logics of knowledge and time could be replaced with an appropriate justification logic.

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First steps towards probabilistic justification logic

Cited by 31 publications

References 13 publications

The complexity of satisfiability in non-iterated and iterated probabilistic logics

The complexity of satisfiability in non-iterated and iterated probabilistic logics

The Complexity of Non-Iterated Probabilistic Justification Logic

Temporal Justification Logic

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