Logics

38 pages, 612 KiB

Open AccessArticle

Distribution-Free Modal Logics: Sahlqvist–Van Benthem Correspondence

by Chrysafis Hartonas

Logics 2025, 3(3), 10; https://doi.org/10.3390/logics3030010 - 15 Aug 2025

We present an extension and generalization of Sahlqvist–van Benthem correspondence to the case of distribution-free modal logic, with, or without negation and/or implication connectives. We follow a reductionist strategy, reducing the correspondence problem at hand to the same problem, but for a suitable system of sorted modal logic (the modal companion of the distribution-free system). The reduction, via a fully abstract translation, builds on the duality between normal lattice expansions and sorted residuated frames with relations (a generalization of classical Kripke frames with relations). The approach is scalable and it can be generalized to other systems, with or without distribution, such as distributive modal logic, or substructural logics with, or without additional modal operators. Full article

26 pages, 2638 KiB

Open AccessArticle

How Explainable Really Is AI? Benchmarking Explainable AI

by Giacomo Bergami and Oliver Robert Fox

Logics 2025, 3(3), 9; https://doi.org/10.3390/logics3030009 - 6 Aug 2025

Viewed by 235

Abstract

This work contextualizes the possibility of deriving a unifying artificial intelligence framework by walking in the footsteps of General, Explainable, and Verified Artificial Intelligence (GEVAI): by considering explainability not only at the level of the results produced by a specification but also considering the explicability of the inference process as well as the one related to the data processing step, we can not only ensure human explainability of the process leading to the ultimate results but also mitigate and minimize machine faults leading to incorrect results. This, on the other hand, requires the adoption of automated verification processes beyond system fine-tuning, which are essentially relevant in a more interconnected world. The challenges related to full automation of a data processing pipeline, mostly requiring human-in-the-loop approaches, forces us to tackle the framework from a different perspective: while proposing a preliminary implementation of GEVAI mainly used as an AI test-bed having different state-of-the-art AI algorithms interconnected, we propose two other data processing pipelines, LaSSI and EMeriTAte+DF, being a specific instantiation of GEVAI for solving specific problems (Natural Language Processing, and Multivariate Time Series Classifications). Preliminary results from our ongoing work strengthen the position of the proposed framework by showcasing it as a viable path to improve current state-of-the-art AI algorithms. Full article

(This article belongs to the Special Issue Logic-Based Methods for Verifiable and Explainable Artificial Intelligence)

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40 pages, 620 KiB

Open AccessArticle

Logics of Statements in Context—First-Order Logic Files

by Uwe Wolter

Logics 2025, 3(3), 8; https://doi.org/10.3390/logics3030008 - 23 Jul 2025

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Abstract

Logics of Statements in Context have been proposed as a general framework to describe and relate, in a uniform and unifying way, a broad spectrum of logics and specification formalisms, which also comprise “open formulas”. In particular, it has been shown that we can define arbitrary first-order “open formulas” in arbitrary categories. At present, there are two deficiencies. In the general case, only signatures with predicate symbols are considered and institutions of statements in context are only defined for single signatures. In this paper, we elaborate the special case of traditional many-sorted first-order logic. We show that any many-sorted first-order signature

Σ

with predicates and (!) operation symbols gives rise to an institution

{FL}_{Σ}

Σ

-statements in context and that any signature morphism results in a comorphism between the corresponding institutions. We prove that we obtain a functor

FL : Sig \to c o I n s

from the category of signatures into the category of institutions and comorphisms. We construct a corresponding Grothendieck institution

{FL}^{♯}

and prove that

{FL}^{♯}

is, indeed, an extension of the traditional institution of first-order logic, which only comprises “closed formulas”. We also investigate substitutions in detail and discuss (elementary) diagrams in the sense of traditional first-order logic. Full article

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12 pages, 212 KiB

Open AccessArticle

Feminist Values and Plumwood’s Account of Logic

by Mansooreh Kimiagari

Logics 2025, 3(3), 7; https://doi.org/10.3390/logics3030007 - 8 Jul 2025

Viewed by 272

Abstract

I aim to examine Val Plumwood’s feminist account of logic, as presented by Plumwood, using the frameworks developed by Elliott and McKaughan, and Intemann. Plumwood argues that relevance logic is the appropriate logical system for feminist reasoning. I intend to assess whether this constitutes a legitimate incorporation of values into logic. To this end, I evaluate the aims of Plumwood as a case study. Additionally, I trace the values embedded in my chosen case to determine whether feminist values advance the epistemic and social objectives of the research. Full article

(This article belongs to the Special Issue Cross-Cultural and Multi-Disciplinary Approaches to the Philosophy of Logic)

63 pages, 583 KiB

Open AccessArticle

Knowability as Continuity: A Topological Account of Informational Dependence

by Alexandru Baltag and Johan van Benthem

Logics 2025, 3(3), 6; https://doi.org/10.3390/logics3030006 - 23 Jun 2025

Viewed by 259

Abstract

We study knowable informational dependence between empirical questions, modeled as continuous functional dependence between variables in a topological setting. We also investigate epistemic independence in topological terms and show that it is compatible with functional (but non-continuous) dependence. We then proceed to study a stronger notion of knowability based on uniformly continuous dependence. On the technical logical side, we determine the complete logics of languages that combine general functional dependence, continuous dependence, and uniformly continuous dependence. Full article

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Logics, Volume 3, Issue 3 (September 2025) – 5 articles

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