On Definability of the Equality in Classes of Algebras with an Equivalence Relation

We present a finitary regularly algebraizable logic not finitely equivalential, for every similarity type. We associate to each of these logics a class of algebras with an equivalence relation, with the property that in this class, the identity is atomatically definable but not finitely atomatically definable. This revised version was published online in June 2006 with corrections to the Cover Date.     

Rhetoric and Dialectic in the Twenty-First Century

The paper presents a historical overview of some characteristic differences between rhetoric and dialectic in the pre-modern tradition. In the light of this historical analysis, some current approaches to dialectic are characterized, with special attention to Ralph Johnson's concept of dialectical tier.     

On the Nature of Continuous Physical Quantities in Classical and Quantum Mechanics

Journal of Philosophical Logic - Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value...     

Term-Modal Logics

Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used in the logics often lack expressiveness to name agents in an intuitive way.To obtain a more expressive language for multi-agent reasoning and a better naming scheme for agents, we introduce a family of logics called term-modal logics. A main feature of our logics is the use of modal operators indexed by the terms of the logics. Thus, one can quantify over variables occurring in modal operators. In term-modal logics agents can be represented by terms, and knowledge of agents is expressed with formulas within the scope of modal operators.This gives us a flexible and uniform language for reasoning about the agents themselves and their knowledge. This article gives examples of the expressiveness of the languages and provides sequent-style and tableau-based proof systems for the logics. Furthermore we give proofs of soundness and completeness with respect to the possible world semantics.     

On Different Intuitionistic Calculi and Embeddings from Int to S4

In this paper, we compare several cut-free sequent systems for propositional intuitionistic logic Intwith respect to polynomial simulations. Such calculi can be divided into two classes, namely single-succedent calculi (like Gentzen's LJ) and multi-succedent calculi. We show that the latter allow for more compact proofs than the former. Moreover, for some classes of formulae, the same is true if proofs in single-succedent calculi are directed acyclic graphs (dags) instead of trees. Additionally, we investigate the effect of weakening rules on the structure and length of dag proofs.The second topic of this paper is the effect of different embeddings from Int to S4. We select two different embeddings from the literature and show that translated (propositional) intuitionistic formulae have sometimes exponentially shorter minimal proofs in a cut-free Gentzen system for S4than the original formula in a cut-free single-succedent Gentzen system for Int. Moreover, the length and the structure of proofs of translated formulae crucially depend on the chosen embedding.     

The Clinical Challenges of Assimilative Integration

S. B. Messer (1992) introduced the notion of assimilative integration in psychotherapy, theorizing that integrative practitioners adhere to their preferred theoretical paradigms while judiciously blending aspects from other models. His assimilative approach offers a conceptual and clinical middle ground between technical eclecticism and a grand, unified theory of psychotherapy. However, the practice of competent assimilative integration is fraught with many challenges, both theoretical and clinical. The goal of the present paper is to explore the challenges of implementing assimilative integration. First, the theoretical and clinical barriers to assimilative approaches are considered. Second, the use of assimilative integration to avoid therapeutic failures is discussed. Finally, a case example is presented to illustrate the author's attempt to assimilate narrative, interpretive interventions within his preferred cognitive–behavioral treatment paradigm.