Converse Ackermann Property and Minimal Negation

A logic S has the Converse Ackermann Property (CAP) if non-necessitive propositions are not derivable in S from necessitive ones. We show in this paper how to introduce minimal negation in positive logics with the CAP. Relational ternary semantics are provided for all the logics considered in this paper

Converse Ackermann property and constructive negation defined with a negation connective

The Converse Ackermann Property is the unprovability of formulas of the form (A -> B) -> C when C does contain neither -> nor ¬. Intuitively, the CAP amounts to rule out the derivability of pure non-necessitive propositions from non-necessitive ones. A constructive negation of the sort historically defined by, e.g., Johansson is added to positive logics with the CAP in the spectrum delimited by Ticket Entailment and Dummett’s logic LC

Cognición, afectividad y sexualidad de la vejez

60 p.[ES] La asignatura "Cognición, afectividad y sexualidad en la vejez" presenta un primer bloque de materiales sobre cognición, que aquí se va a concentrar en el razonamiento adulto. El ejercicio del razonamiento es un elemento esencial en el envejecimento activo y en esta asignatura, en primer lugar, se estudia la fundamentación del alcance de los distintos tipos de razonamiento sobre la mente que envejece. En segundo lugar se aportan simplificadamente los instrumentos técnicos de producción y evaluación de razonamientos de tipo deductivo, probabilístico, ordinario, rebatible, y práctico. Finalmente, en tercer lugar, se elaboran para los profesionales cuadernos de razonamiento que se integran en programas de envejecimiento activo. La labor de fundamentación teórica se resume en (1). Dos cuadernos de razonamiento se detallan argumentadamente en (2) y (3). La asignatura además entrega durante su impartición materiales técnicos para la elaboración y evaluación de razonamientos. Por tanto el presente material se organiza en los siguientes apartados: 1. La razón que envejece: aspectos neurales, psicológicos y lógicos. 2. Cuaderno de razonamiento deductivo. 3. Haciendo lo mejor: ejemplificación de un cuaderno de razonamiento práctico adulto

The P-W problem

This thesis investigates the properties of two systems of pure implication, with axioms a~d rules corresponding to the principles of transitivity of implication in the one system, and these axioms and rules plus the law of identity in the other. The main part of the text is devoted to a semantic analysis of these two systems. A class of models, called S-models, is defined and studied. The original construction of these S-models is due to R.K. Meyer. They derive t heir strength and interest from the fact that they employ a three-valued interpretation of the metalogical operations. By suitably determining the notion of validity using these three values, both of the systems mentioned above can be accommodated at once within the same class of models. The results obtained include soundness and completeness, decidability, arid, most importantly, the solution to a problem posed by Anderson and Belnap in their treatise, Entailment (Princeton U.P. 1975). Briefly, it is shown that, in the system o f pure transitivity axioms (and corresponding rules) , no instance of the axiom of identity is provable. When the axiom of identity is added to the system , one obtains as a corresponding result that no two distinct formulas co-entail each other