A survey of paraconsistent logics that are prominent representatives of the different approaches that have been followed to develop paraconsistent logics is provided. The paraconsistent logics that will be discussed are an enrichment of Priest’s logic LP, the logic RM3 from the school of relevance logic, da Costa’s logics Cn, Jaskowski’s logic D2, and Subrahmanian’s logics Ptau. A deontic logic based on the first of these logics will be discussed as well. Moreover, some proposed adaptations of the AGM theory of belief revision to paraconsistent logics will be mentioned.

Topologically ordered systems play a prominent role in current research in condensed matter physics; examples include systems that exhibit the quantum Hall effect, topological insulators, and topological superconductors. These systems possess properties that are characterized by topological invariants, exhibit phase transitions that cannot be characterized by spontaneous symmetry breaking, and exhibit order that cannot be characterized in terms of a local order parameter. They thus fall outside the scope of the Landau–Ginsburg theory of phase transitions, which, arguably, has informed much of the discussion, in both the physics and philosophy literature, of emergence in condensed matter systems. Nevertheless, some authors have claimed that topologically ordered systems exhibit emergence.

Analogues of Scott’s isomorphism theorem, Karp’s theorem as well as results on lack of compactness and strong completeness are established for infinitary propositional relevant logics. An “interpolation theorem” (of a particular sort introduced by Barwise and van Benthem) for the infinitary quantificational boolean logic L∞ω holds. This yields a preservation result characterizing the expressive power of infinitary relevant languages with absurdity using the model-theoretic relation of relevant directed bisimulation as well as a Beth definability property.

When you first learned about functions, they were most likely introduced as abstractions of expressions. For example, consider the expression 2 + 3, which can be immediately evaluated by the rules of elementary arithmetic to give value 5. We can abstract, i.e., generalize the notion of “adding 3 to 2” to that of “adding 3 to something,” giving rise the function f : x 7→ x + 3. We can then apply this function to other arguments, e.g., f(4) = 4 + 3 = 7. This style of function definition is intentional—functions are defined by specifying an intended means of evaluation. Later, you may have been encouraged to think of functions extensionally, i.e., as sets of ordered pairs, e.g. f = {(x, y) : y = x + 3}. Such an approach conveys substantial metamathematical advantages, but it comes at a terrible cost—functions are no longer things that you can compute with. The lambda calculus [Chu41] returns to the notion of functions as abstractions of expressions. Abstraction is accomplished by the eponymous lambda (λ), by means of which we could define the function f as λx. x + 3. An abstraction may be applied to an argument,

El presente trabajo tiene un carácter meramente exploratorio y trata de responder a la pregunta ¿qué es lenguaje? No trata de responderla de manera directa lo que supondría un sistema filosófico bien establecido. Y aunque sin abandonar el carácter sistemático de cualquier filosofía se enfrenta al tema de manera indirecta respondiendo ¿qué cosas tienen que ver con el lenguaje?, y ¿cómo organizarlas? Planteadas así las cosas parece que el lenguaje lo recubre todo. Pero es evidente por otra parte, que todo no es lenguaje.

This paper is a reply from an intuitionistic point of view to three criticisms made by Vuillemin [[4], pp. 8-14] against Prior’s logical reconstruction of Diodorus’ Master Argument (for short “Diodorus-Prior’s proof”). Indeed, the intuitionistic interpretation of Prior’s proof can rule out the first two criticisms and limit the scope of the third. Last, we prove that the conclusion of Diodorus’ Master Argument can be deduced from only one undischarged assumption, i.e. premise (A). This new proof is therefore an improvement of Didorus-Prior’s, because it shows clearly that premise (A) is incompatible with premise (C).

The motivation for this paper arises in part from the teaching experience of its author. This does not suggest that it will be of a pedagogical nature. Quite to the contrary: we shall have to go back to first principles. But its rather unorthodox proposals wil so we hope appear less astonishing when they are seen against this background. Our pedagogical task was to teach logic to several hundreds of undergraduates in the social sciences, psychology and the humanities. Accepting such a task means believing logic to be relevant for this heterogeneous audience.

The group of units modulo constants of an affine variety over an algebraically closed field is free abelian of finite rank. Computing this group is difficult but of fundamental importance in tropical geometry, where it is desirable to realize intrinsic tropicalizations. We present practical algorithms for computing unit groups of smooth curves of low genus. Our approach is rooted in divisor theory, based on interpolation in the case of rational curves and on methods from algebraic number theory in the case of elliptic curves.

Le concept de totalite en tant que totalite organique, interesse Piaget des l’apparition de Recherche(1918). Ce concept implique logiquement ‘ etude du probleme de la relation entre la partie et Ie tout.! Dans son autobiographie (1976), Piaget affirme que “(. .. ) dans tous les domaines de la vie (organique, mentale, sociale) il existe des “totalites qualitativement distinctes de leurs parties et qui leur imposent une organisation. Par consequent il n ‘existe pas d’elements isoles.

Propongo una crítica a la noción de serialidad en la comprensión del concepto de tiempo en el contexto de los estudios cartesianos. En el debate entre los defensores del tiempo continuo y quienes defienden un tiempo discreto, sostengo que ninguna de estas posiciones tiene en cuenta que la serialidad se enmarca en una noción de tiempo que se concibe como divisible y numerable y que no pertenece intrínsecamente a la naturaleza de la experiencia temporal del cogito. Mi propuesta consiste en comenzar a desarrollar la caracterización de dicho tiempo experiencial y cogitativo.