Logics for reasoning about degrees of confirmation

Sejla Dautovic; Dragan Doder; Zoran Ognjanovic

doi:10.1093/logcom/exab033

Logics for reasoning about degrees of confirmation

Sejla Dautovic, Dragan Doder^*, Zoran Ognjanovic

^*Corresponding author for this work

Sub Intelligent Systems

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Abstract

In this paper, we present a first-order and a propositional logic for reasoning about degrees of confirmation. We define the appropriate formal languages and describe the corresponding classes of models. We provide infinitary axiomatizations for both logics and we prove that the axiomatizations are sound and strongly complete. We also show that our propositional logic is decidable. For some restrictions of the logics, we provide finitary axiomatic systems.

Original language	English
Pages (from-to)	2189-2217
Number of pages	29
Journal	Journal of Logic and Computation
Volume	31
Issue number	8
DOIs	https://doi.org/10.1093/logcom/exab033
Publication status	Published - Dec 2021

Keywords

probabilistic logic
measure of confirmation
completeness theorem
decidability

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10.1093/logcom/exab033

exab033Final published version, 318 KBLicence: Taverne

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title = "Logics for reasoning about degrees of confirmation",

abstract = "In this paper, we present a first-order and a propositional logic for reasoning about degrees of confirmation. We define the appropriate formal languages and describe the corresponding classes of models. We provide infinitary axiomatizations for both logics and we prove that the axiomatizations are sound and strongly complete. We also show that our propositional logic is decidable. For some restrictions of the logics, we provide finitary axiomatic systems.",

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AU - Dautovic, Sejla

AU - Doder, Dragan

AU - Ognjanovic, Zoran

PY - 2021/12

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N2 - In this paper, we present a first-order and a propositional logic for reasoning about degrees of confirmation. We define the appropriate formal languages and describe the corresponding classes of models. We provide infinitary axiomatizations for both logics and we prove that the axiomatizations are sound and strongly complete. We also show that our propositional logic is decidable. For some restrictions of the logics, we provide finitary axiomatic systems.

AB - In this paper, we present a first-order and a propositional logic for reasoning about degrees of confirmation. We define the appropriate formal languages and describe the corresponding classes of models. We provide infinitary axiomatizations for both logics and we prove that the axiomatizations are sound and strongly complete. We also show that our propositional logic is decidable. For some restrictions of the logics, we provide finitary axiomatic systems.

KW - probabilistic logic

KW - measure of confirmation

KW - completeness theorem

KW - decidability

U2 - 10.1093/logcom/exab033

DO - 10.1093/logcom/exab033

M3 - Article

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VL - 31

SP - 2189

EP - 2217

JO - Journal of Logic and Computation

JF - Journal of Logic and Computation

IS - 8

ER -

Logics for reasoning about degrees of confirmation

Abstract

Keywords

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