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Document type
Journal articles

Document subtype
Full paper

Probabilistic logic over equations and domain restrictions

Participants in the publication
Andreia Mordido (Author)
Dep. Informática
Carlos Caleiro (Author)

We propose and study a probabilistic logic over an algebraic basis, including equations and domain restrictions. The logic combines aspects from classical logic and equational logic with an exogenous approach to quantitative probabilistic reasoning. We present a sound and weakly complete axiomatization for the logic, parameterized by an equational specification of the algebraic basis coupled with the intended domain restrictions.We show that the satisfiability problem for the logic is decidable, under the assumption that its algebraic basis is given by means of a convergent rewriting system, and, additionally, that the axiomatization of domain restrictions enjoys a suitable subterm property. For this purpose, we provide a polynomial reduction to Satisfiability Modulo Theories. As a consequence, we get that validity in the logic is also decidable. Furthermore, under the assumption that the rewriting system that defines the equational basis underlying the logic is also subterm convergent, we show that the resulting satisfiability problem is NP-complete, and thus the validity problem is coNP-complete. We test the logic with meaningful examples in information security, namely by verifying and estimating the probability of the existence of offline guessing attacks to cryptographic protocols.

Date of Publication

Where published
Mathematical Structures in Computer Science

Publication Identifiers
ISSN - 0960-1295
eISSN - 1469-8072

Cambridge University Press (CUP)

Number of pages
Starting page
Last page

Document Identifiers

SCIMAGO Q3 (2018) - 0.371 - Mathematics (miscellaneous)
Google Metrics (2018) - 21

Satisfiability problem Equational logic Probabilistic logic Offline guessing attacks


Andreia Mordido, Carlos Caleiro, (2019). Probabilistic logic over equations and domain restrictions. Mathematical Structures in Computer Science, 1-24. ISSN 0960-1295. eISSN 1469-8072.

Andreia Mordido, Carlos Caleiro, "Probabilistic logic over equations and domain restrictions" in Mathematical Structures in Computer Science, pp. 1-24, 2019. 10.1017/s096012951800035x

@article{35846, author = {Andreia Mordido and Carlos Caleiro}, title = {Probabilistic logic over equations and domain restrictions}, journal = {Mathematical Structures in Computer Science}, year = 2019, pages = {1-24}, }