Weakly Associative Relation Algebras with Polyadic Composition Operations

In this paper we introduced various classes of weakly associative relation algebras with polyadic composition operations. Among them is the class RWA of representable weakly associative relation algebras with polyadic composition operations. Algebras of this class are relativized representable relation algebras augmented with an infinite set of operations of increasing arity which are generalizations of the binary relative composition. We show that RWA is a canonical variety whose equational theory is decidable.     

Linearization of the BCK-logic

In the paper we obtain a new characterization of the BCK-algebras which are subdirect product of BCK-chains. We give an axiomatic algebraizable extension of the BCK-calculus, by means of a recursively enumerable set of axioms, such that its equivalent algebraic semantics is definitionally equivalent to the quasivariety of BCK-algebras generated by the BCK-chains. We propose the concept of "linearization of a system" and we give some examples.     

From reasonable preferences,via argumentation,to logic

This article demonstrates that typical restrictions which are imposed in dialogical logic in order to recover first-order logical consequence from a fragment of natural language argumentation are also forthcoming from preference profiles of boundedly rational players, provided that these players instantiate a specific player type and compute partial strategies. We present two structural rules, which are formulated similarly to closure rules for tableaux proofs that restrict players' strategies to a mapping between games in extensive forms (i.e., game trees) and proof trees. Both rules are motivated from players' preferences and limitations; they can therefore be viewed as being player-self-imposable. First-order logical consequence is thus shown to result from playing a specific type of argumentation game. The alignment of such games with the normative model of the Pragma-dialectical theory of argumentation is positively evaluated. But explicit rules to guarantee that the argumentation game instantiates first-order logical consequence have now become gratuitous, since their normative content arises directly from players' preferences and limitations. A similar naturalization for non-classical logics is discussed.     

Clinical applications of Matte Blanco's thinking

Ignacio Matte Blanco (1908–1995) left very few specific indications about the applications of his theoretical notions to his interpretative style. The author shows how he uses Matte Blanco to formulate some of his own interpretations. The first part of the paper uses clinical vignettes to illustrate some of Matte‐Blanco's concepts. Their theoretical vocabulary is thus made explicit. Then two psychoanalytic sessions are discussed at greater length, together with one from a therapy, so that the use of Matte‐Blanco's notions can be seen clearly, allowing for a fresh perspective on areas of psychoanalytic theory, particularly dreams, psychopathology viewed according to the proportions of asymmetrical and symmetrical functioning in the patient's bi‐logical mental system, the multidimensionality of the unconscious, the structural unconscious, the emotion‐thought relationship, projective identification, resistance, and negative therapeutic reaction. The practical consequences of all this are elaborated, particularly the ensuing possibility of ‘thinking with the patient' in the session. This enables the patient to introject a form of mental functioning in which the asymmetrical mode is not invaded by the symmetric mode (a parallel can be seen here with the Bionian concept of dialogue between the psychotic and non‐psychotic parts of the mind).     

Truth Analysis of the Gettier Argument

Gettier (1963) presented the now famous Gettier problem as a challenge to epistemology. The methods Gettier used to construct his challenge, however, utilized certain principles of formal logic that are actually inappropriate for the natural language discourse of the Gettier cases. In that challenge to epistemology, Gettier also makes truth claims that would be considered controversial in analytic philosophy of language. The Gettier challenge has escaped scrutiny in these other relevant academic disciplines, however, because of its façade as an epistemological analysis. This article examines Gettier's methods with the analytical tools of logic and analytic philosophy of language.     

Temporal logics for concurrent recursive programs: Satisfiability and model checking

We develop a general framework for the design of temporal logics for concurrent recursive programs. A program execution is modeled as a partial order with multiple nesting relations. To specify properties of executions, we consider any temporal logic whose modalities are definable in monadic second-order logic and which, in addition, allows PDL-like path expressions. This captures, in a unifying framework, a wide range of logics defined for ranked and unranked trees, nested words, and Mazurkiewicz traces that have been studied separately. We show that satisfiability and model checking are decidable in EXPTIME and 2EXPTIME, depending on the precise path modalities.     

The existence of superluminal particles is consistent with relativistic dynamics

Within an axiomatic framework, we prove that the existence of faster than light (FTL) particles is consistent with (does not contradict) the dynamics of Einstein's special relativity. The proof goes by constructing a model of relativistic dynamics where FTL particles can move with arbitrary speeds. To have a complete picture, we not only construct an appropriate model but explicitly list all the basic assumptions (axioms) we use.     

Continuity and geometric logic

This paper is largely a review of known results about various aspects of geometric logic. Following Grothendieckʼs view of toposes as generalized spaces, one can take geometric morphisms as generalized continuous maps. The constructivist constraints of geometric logic guarantee the continuity of maps constructed, and can do so from two different points of view: for maps as point transformers and maps as bundles.