Transfers between Logics and their Applications

In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attributes such as consequence operator, syntactical structure, and internal transformations. In particular, we treat Belief Revision Systems (BRS) as our main example, defining the Wide Belief Revision Systems (WBRS's). This generalization allows us to define BRS's in an abstract setting for classical and non-standard logics. We also show how the concept of translation between logics can be obtained as a particular case of transfers.     

Treatment of Comorbid Pica and Generalized Anxiety Disorder: A Case Study

This case report describes the assessment and treatment of a treatment-naïve 36-year-old Hispanic/Latina female with comorbid pica and generalized anxiety disorder (GAD), and iron-deficiency anemia. At the onset of treatment, the client consumed chalkboard chalk and vermiculite from potting soil approximately three times per week and presented with moderate-severity GAD. Assessment and treatment occurred over 24 weekly outpatient individual sessions. Treatment was delivered in concert with medical intervention to address anemia. A cognitive-behavioral case formulation was developed from multiple assessment sources. A process-based cognitive-behavioral therapy (CBT) intervention approach was used to target GAD and pica simultaneously, which included psychoeducation, self-monitoring, arousal reduction skills, cognitive training (reappraisal, distancing), and behavior modification/stimulus control techniques. Barriers to treatment and their solutions are discussed. At the end of treatment, the client demonstrated increased insight and understanding of her worry symptoms and pica behavior, acquired cognitive skills and arousal reduction strategies for managing GAD, and reported less than one episode of pica per week. The identified assessment and treatment approach is worthy of future investigation to inform empirically based treatment development efforts, especially for pica.     

Hilbert-style Presentations of Two Logics Associated to Tetravalent Modal Algebras

We analyze the variety of A. Monteiro’s tetravalent modal algebras under the perspective of two logic systems naturally associated to it. Taking profit of the contrapositive implication introduced by A. Figallo and P. Landini, sound and complete Hilbert-style calculi for these logics are presented.     

Non-Commutative Topology and Quantales

The relationship between q-spaces (c.f. [9]) and quantum spaces (c.f. [5]) is studied, proving that both models coincide in the case of Spec A, the spectrum of a non-commutative C*-algebra A. It is shown that a sober T ₁ quantum space is a classical topological space. This difficulty is circumvented through a new definition of point in a quantale. With this new definition, it is proved that Lid A has enough points. A notion of orthogonality in quantum spaces is introduced, which permits us to express the usual topological properties of separation. The notion of stalks of sheaves over quantales is introduced, and some results in categorial model theory are obtained.     

Valuation Semantics for First-Order Logics of Evidence and Truth

This paper introduces the logic QLET_F, a quantified extension of the logic of evidence and truth LET_F, together with a corresponding sound and complete first-order non-deterministic valuation semantics. LET_F is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (FDE) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘A entails that A behaves classically, ∙A follows from A’s violating some classically valid inferences. The semantics of QLET_F combines structures that interpret negated predicates in terms of anti-extensions with first-order non-deterministic valuations, and completeness is obtained through a generalization of Henkin’s method. By providing sound and complete semantics for first-order extensions of FDE, K3, and LP, we show how these tools, which we call here the method of anti-extensions + valuations, can be naturally applied to a number of non-classical logics.