Probabilistic Justification Logic

Kokkinis, Ioannis; Ognjanović, Zoran; Studer, Thomas

doi:10.1007/978-3-319-27683-0_13

Cited by 22 publications

(31 citation statements)

References 14 publications

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“…As a continuation of [15] and [16] we showed that results for justification logic and probabilistic logic can be nicely combined. Recall that the probabilistic justification logic PJ is obtained by adding probability operators to the justification logic J.…”

Section: Final Remarks and Conclusionmentioning

confidence: 70%

“…Observe that by Theorem 9 and our previous remarks we have that, for a decidable schematic and axiomatically apropriate constant specification, the derivability problem for the logic PJ CS is Π p 2 -complete. In [16] the probabilistic justification logic PPJ is defined. PPJ is a natural extension of PJ that supports iterations of the probability operator as well as justifications over probabilities.…”

Section: Final Remarks and Conclusionmentioning

confidence: 99%

“…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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Section: Final Remarks and Conclusionmentioning

confidence: 70%

Section: Final Remarks and Conclusionmentioning

confidence: 99%

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 of justification graphs axiomatised in Section 3. Our logic and its axiomatisation incorporates a partial order on the set of beliefs that underlies their prioritization during conflict resolution, which contrasts with the probabilistic extension of justification logic outlined in [22].…”

Section: Related Workmentioning

confidence: 99%

Dynamic Conflict Resolution Using Justification Based Reasoning

Damm¹,

Fränzle²,

Hagemann³

et al. 2019

Electron. Proc. Theor. Comput. Sci.

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We study conflict situations that dynamically arise in traffic scenarios, where different agents try to achieve their set of goals and have to decide on what to do based on their local perception. We distinguish several types of conflicts for this setting. In order to enable modelling of conflict situations and the reasons for conflicts, we present a logical framework that adopts concepts from epistemic and modal logic, justification and temporal logic. Using this framework, we illustrate how conflicts can be identified and how we derive a chain of justifications leading to this conflict. We discuss how conflict resolution can be done when a vehicle has local, incomplete information, vehicle to vehicle communication (V2V) and partially ordered goals.

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“…because this coin looks similar to a counterfeit coin I have seen some time ago". As another application of PPJ, in [19] we have shown that the lottery paradox [23] can be analysed in this logic. The lottery paradox goes as follows: assume that we have 1, 000 tickets in a lottery where every ticket has the same probability to win and there is exactly one winning ticket.…”

Section: Background and Related Workmentioning

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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Probabilistic Justification Logic

Cited by 22 publications

References 14 publications

The Complexity of Non-Iterated Probabilistic Justification Logic

The Complexity of Non-Iterated Probabilistic Justification Logic

Dynamic Conflict Resolution Using Justification Based Reasoning

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

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