Logics, Volume 3, Issue 4 (December 2025) – 6 articles

Traditional degree semantics approaches have aimed to pin down the inherent class of adjectives. This paper presents a novel dynamic perspective, where the classification of an adjective is dynamic and syntactically dependent. Using measurement theory and fuzzy set analysis, the proposed framework defines dynamic patterns of adjective classes with a set of axioms and integrates these patterns with syntactic structures to explain the flexibility and constraints observed in adjectival expressions. Employing Mandarin data, the paper illustrates how different syntactic constructions select specific adjective classes, thereby affecting their distribution and interpretation. This approach not only accommodates cross-linguistic variations but also provides a more comprehensive understanding of the semantics of adjectives. Full article

We offer a framework that captures both context-dependency and vagueness of predicate meanings—illustrated by the politically relevant case of woman—as an interaction of lexical meaning and Question under Discussion (‘QUD’). We extend existing approaches to non-maximality to superficially polysemous predicates like woman and show that this is conceptually coherent and insightful for a linguistic analysis of political debates about gender invitation policies: while there are (i) clear, semantically true, and (ii) strictly unacceptable cases of x is a woman, there are also (iii) merely pragmatically acceptable cases (‘like a woman with respect to the QUD’) as well as (iv) truly vague ones. We argue that this four-way division is the least complex model that captures current gender discourses in a harm-reducing, trans-inclusive way. This offers a new perspective on the semantics–pragmatics interface of predicate meanings. Full article

José Morgado introduced in 1962 a novel notion of hyperlattices, which he called reticuloides. In his master’s thesis submitted in 1971 (under the supervision of Newton da Costa), Antonio M. Sette introduced a new class of implicative hyperlattices (here called SIHLs) based on Morgado’s hyperlattices. He also extended SIHLs by adding a unary hyperoperator, thus defining a class of hyperalgebras (denoted ${\mathrm{SHC}}_{\omega }$) corresponding to da Costa algebras for $C_{\omega }$, thereby providing suitable semantics for the logic $C_{\omega }$. In this paper, after providing a (hyper)lattice-theoretic characterization of Sette’s implicative hyperlattices and proving some basic results on SIHLs, we introduce a class of swap structures—special hyperalgebras over the signature of $C_{\omega }$ that arise naturally from implicative lattices. We prove that these swap structures are indeed ${\mathrm{SHC}}_{\omega }$. Finally, we demonstrate that the class ${\mathrm{SHC}}_{\omega }$, as well as the aforementioned swap structures, characterizes the logic $C_{\omega }$. Full article

If one believes that $2+2=4$, then one also believes that either $2+2=4$ or 971 is a cousin prime number. This follows from doxastic logics based on standard Kripke relational semantics, which validate disjunction introduction for belief. However, this principle does not hold in topic-sensitive semantics. An agent who lacks the concept of a ‘cousin prime number’ may be unable to entertain, and thus unable to believe, any proposition involving that concept. I argue that while disjunction introduction may fail for belief—and for other epistemic states that presuppose belief—it does hold for certain states that do not require belief. In this paper, I focus on the notion of commitment to the truth. Drawing on the concept of logical grounding, I propose formal semantics that preserve the requirement of topic-grasping, but weaken it in a way that allows for a more standard treatment of disjunction. Full article

Rationality has long been considered the quintessence of humankind. However, psychological experiments revealing reliable divergences in performances on reasoning tasks from normative principles of reasoning have cast serious doubt on the venerable dogma that human beings are rational animals. According to the standard picture, reasoning in accordance with principles based on rules of logic, probability theory, etc., is rational. The standard picture provides the backdrop for both the rationality and irrationality thesis, and, by virtue of the competence-performance distinction, diametrically opposed interpretations of reasoning experiments are possible. However, the standard picture rests on shaky foundations. Jean Piaget developed a psychological theory of reasoning, in which logic and mathematics are continuous with psychology but nevertheless autonomous sources of knowledge. Accordingly, logic, probability theory, etc., are not extra-human norms, and reasoners have the ability to reason in accordance with them. In this paper, I set out Piaget’s theory of rationality, using intra- and interpropositional reasoning as illustrations, and argue that Piaget’s theory of rationality is compatible with the standard picture but actually undermines it by denying that norms of reasoning based on logic are psychologically relevant for rationality. In particular, rather than logic being the normative benchmark, I argue that rationality according to Piaget has a psychological foundation, namely the reversibility of the operations of thought constituting cognitive structures. Full article

Analogies are an important part of human cognition for learning and discovering new concepts. There are many different approaches to defining analogies and how new ones can be found or constructed. We propose a novel approach in the tradition of structure mapping using colored multigraphs to represent domains. We define a category of colored multigraphs in order to utilize some Category Theory (CT) concepts. CT is a powerful tool for describing and working with structure-preserving maps. There are many useful applications for this theory in cognitive science, and we want to introduce one such application to a broader audience. CT and the concepts used in this paper are introduced and explained. We show how the category theoretical concepts product and pullback can be used with the category of colored multigraphs to find possible analogies between domains using different requirements. The dual notion of a pullback, the pushout, is then used as conceptual blending to generate a new domain. Full article