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Logics, Volume 3, Issue 2 (June 2025) – 4 articles

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15 pages, 368 KiB  
Article
Multi-Fidelity Temporal Reasoning: A Stratified Logic for Cross-Scale System Specifications
by Ali Baheri and Peng Wei
Logics 2025, 3(2), 5; https://doi.org/10.3390/logics3020005 - 3 Jun 2025
Viewed by 156
Abstract
We present Stratified Metric Temporal Logic (SMTL), a novel formalism for specifying and verifying the properties of complex cyber–physical systems that exhibit behaviors across multiple temporal and abstraction scales. SMTL extends existing temporal logics by incorporating a stratification operator, [...] Read more.
We present Stratified Metric Temporal Logic (SMTL), a novel formalism for specifying and verifying the properties of complex cyber–physical systems that exhibit behaviors across multiple temporal and abstraction scales. SMTL extends existing temporal logics by incorporating a stratification operator, enabling the association of temporal properties with specific abstraction levels. This allows for the natural expression of multi-scale requirements while maintaining formal reasoning about inter-level relationships. We formalize the syntax and semantics of SMTL, proving that it strictly subsumes metric temporal logic (MTL) and offers enhanced expressiveness by capturing properties unattainable in existing logics. Numerical simulations comparing agents operating under MTL and SMTL specifications show that SMTL enhances agent coordination and safety, reducing collision rates without substantial computational overhead or compromising path efficiency. These findings highlight SMTL’s potential as a valuable tool for designing and verifying complex multi-agent systems operating across diverse temporal and abstraction scales. Full article
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18 pages, 297 KiB  
Article
Algorithmic Problems for Computation Trees
by Mikhail Moshkov
Logics 2025, 3(2), 4; https://doi.org/10.3390/logics3020004 - 9 May 2025
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Abstract
In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The satisfiability problem is concerned with recognizing sentences that are true in at least [...] Read more.
In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The satisfiability problem is concerned with recognizing sentences that are true in at least one structure from a given set of structures. We study how the decidability of the optimization problem depends on the decidability of the solvability and satisfiability problems. We also consider various examples with both decidable and undecidable solvability and satisfiability problems. Full article
30 pages, 530 KiB  
Article
Distribution-Free Normal Modal Logics
by Chrysafis Hartonas
Logics 2025, 3(2), 3; https://doi.org/10.3390/logics3020003 - 1 Apr 2025
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Abstract
This article initiates the semantic study of distribution-free normal modal logic systems, laying the semantic foundations and anticipating further research in the area. The article explores roughly the same area, though taking a different approach, as a recent article by Bezhanishvili, de Groot, [...] Read more.
This article initiates the semantic study of distribution-free normal modal logic systems, laying the semantic foundations and anticipating further research in the area. The article explores roughly the same area, though taking a different approach, as a recent article by Bezhanishvili, de Groot, Dmitrieva and Morachini, who studied a distribution-free version of Dunn’s positive modal logic (PML). Unlike PML, we consider logics that may drop distribution and that are equipped with both an implication connective and modal operators. We adopt a uniform relational semantics approach, relying on recent results on representation and duality for normal lattice expansions. We prove canonicity and completeness in the relational semantics of the minimal distribution-free normal modal logic, assuming just the K-axiom, as well as those of its axiomatic extensions obtained by adding any of the D, T, B, S4 or S5 axioms. Adding distribution can be easily accommodated and, as a side result, we also obtain a new semantic treatment of intuitionistic modal logic. Full article
5 pages, 189 KiB  
Article
On a Correspondence Between Two Kinds of Bilateral Proof-Systems
by Nissim Francez
Logics 2025, 3(2), 2; https://doi.org/10.3390/logics3020002 - 24 Mar 2025
Viewed by 212
Abstract
The paper shows the deductive equivalence between bilateral (and multilateral) proof systems based on signed formulas and proof systems based on multiple derivability relations. Full article
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