Q-valued sets are non-classical models of the formalized theory of identity with existence predicate based on the axioms of a non-commutative and non-idempotent logic. The singleton monad on the category of Q-valued sets is constructed, and elementary properties of T-algebras of the singleton monad are investigated.

Possibility studies is an emerging field of research including topics as diverse as creativity, imagination, innovation, anticipation, counterfactual thinking, wondering, the future, social change, hope, agency, and utopia. The Possible: A Sociocultural Theory contributes to this wide field by developing a sociocultural account of the possible grounded in the notions of difference, position, perspective, dialogue, action, and culture.

This article studies the ambitions involved in founding the European Association of Experimental Social Psychology (EAESP) in the context of a differentiation between social psychology practised in Europe on the one hand and the United States on the other. To this end 8 key actors have been interviewed: 4 members of the very first Executive Committee (or Planning Committee as it was called then) as well as 4 key players of a second generation. Also the EAESP’s archives have been consulted. (...) Moreover, data regarding the developments of EAESP’s membership and EAESP’s house journal, the European Journal of Social Psychology (EJSP), were used to assess to what extent the ambitions in developing a European social psychology have been realized. The conclusion is that, despite various successes, it remains questionable whether the founders’ aims have been fulfilled. (shrink)

Hans-Jørgen Schanz (1948-2022) har i mere end 50 år været en af de mest tænksomme og væsentlige danske intellektuelle, og han var samtidig som professor den bærende og ikke mindst samlende kraft på Idéhistorie ved Aarhus Universitet. Forskningsmæssigt spændte han meget vidt over områder som metafysik, modernitet, politisk filosofi, kunstfilosofi, religionsfilosofi og teologi. Han har begået omkring 40 bøger og et utal af artikler, og han havde en uforlignelig beundringsværdig evne til at tænke selv og insisterede gennem hele sit årelange (...) virke på, at tænkningen skulle være båret af ånd. Han var derudover en meget skattet foredragsholder på højskoler, sognegårde, Folkeuni-versitetet, teologiske konventer og efter- og videreuddannelsesregi. (shrink)

Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of (...) handling duality. (shrink)

We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes...

Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of (...) handling duality. (shrink)

Each Girard quantale provides a support for a semantics for linear propositional formulas. Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group. In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of handling duality.

The system GLS, which is a modal sequent calculus system for the provability logic GL, was introduced by G. Sambin and S. Valentini in Journal of Philosophical Logic, 11, 311–342,, and in 12, 471–476,, the second author presented a syntactic cut-elimination proof for GLS. In this paper, we will use regress trees in order to present a simpler and more intuitive syntactic cut derivability proof for GLS1, which is a variant of GLS without the cut rule.

The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De Morgan (...) monoids may be mapped by noninjective homomorphisms. The homomorphic preimages of C4 within DMM constitute a proper quasivariety, which is shown to have a largest subvariety U. The covers of the variety within U are revealed here. There are just ten of them. In exactly six of these ten varieties, all nontrivial members have C4 as a retract. In the varietal join of those six classes, every subquasivariety is a variety—in fact, every finite subdirectly irreducible algebra is projective. Beyond U, all covers of [or of ] within DMM are discriminator varieties. Of these, we identify infinitely many that are finitely generated, and some that are not. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids. (shrink)

Monoidal triangular norm logic MTL is the logic of left-continuous triangular norms. In the paper we present a relational formalization of the logic MTL and then we introduce relational dual tableau that can be used for verification of validity of MTL-formulas. We prove soundness and completeness of the system.

The notion of a natural numbers object in a monoidal category is defined and it is shown that the theory of primitive recursive functions can be developed. This is done by considering the category of cocommutative comonoids which is cartesian, and where the theory of natural numbers objects is well developed. A number of examples illustrate the usefulness of the concept.

We prove that every Turing degree a bounding some non-GL₂ degree is recursively enumerable in and above (r.e.a.) some 1-generic degree.

Dynamic Predicate Logic (DPL) is a variant of Predicate Logic introduced by Groenendijk and Stokhof. One rationale behind the introduction of DPL is that it is closer to Natural Language than ordinary Predicate Logic in the way it treats scope.In this paper I develop some variants of DPL that can more easily approximate Natural Language in some further aspects. Specifically I add flexibility in the treatment of polarity and and some further flexibility in the treatment of scope.I develop a framework (...) that is intended to encourage further experimentation with alternative variants of DPL. In this framework the new meanings are, roughly,indexed sets of old meanings. The indices can be viewed as "files'' or "storage devices.''Each such file supports a separate "information stream.''The interaction of the new meanings is "programmed'' with the help of certain monoids acting on the indices. The construction of the new meanings can be viewed as an application of the Grothendieck Construction to monoids. (shrink)

ABSTRACTMonoidal logics were introduced as a foundational framework to analyze the proof theory of logical systems. Inspired by Lambek's seminal work in categorical logic, the objective is to defin...

Dynamical systems are mathematical structures whose aim is to describe the evolution of an arbitrary deterministic system through time, which is typically modeled as (a subset of) the integers or the real numbers. We show that it is possible to generalize the standard notion of a dynamical system, so that its time dimension is only required to possess the algebraic structure of a monoid: first, we endow any dynamical system with an associated graph and, second, we prove that such a (...) graph is a category if and only if the time model of the dynamical system is a monoid. In addition, we show that the general notion of a dynamical system allows us not only to define a family of meaningful dynamical concepts, but also to distinguish among a cluster of otherwise tangled notions of reversibility, whose logical relationships are finally analyzed. (shrink)

Monoidal logics were introduced as a foundational framework to analyse the proof theory of deontic logic. Building on Lambek’s work in categorical logic, logical systems are defined as deductive systems, that is, as collections of equivalence classes of proofs satisfying specific rules and axiom schemata. This approach enables the classification of deductive systems with respect to their categorical structure. When looking at their proof theory, however, one can see that there are similarities between monoidal and substructural logics. The purpose of (...) the present paper is to address this issue and highlight the differences between these two approaches. We argue that monoidal logics provide a more flexible foundational framework that enables a finer analysis of the relationship between negation and other logical connectives. We show that the elimination of double negation is independent from the de Morgan dualities, that monoidal deductive systems are not necessarily weakly distributive and that deduc... (shrink)

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. A part of the so-called Gelfand–Naimark–Segal (GNS) construction is identified as an isomorphism of categories, relating states on involutive monoids and inner products. This correspondence exists in arbritrary involutive symmetric (...) monoidal categories. (shrink)

We show how to reconstruct the topology on the monoid of endomorphisms of the rational numbers under the strict or reflexive order relation, and the polymorphism clone of the rational numbers under the reflexive relation. In addition we show how automatic homeomorphicity results can be lifted to polymorphism clones generated by monoids.