A Formal Characterisation of Hamblin’s Action-State Semantics

Hamblin’s Action-State Semantics provides a sound philosophical foundation for understanding the character of the imperative. Taking this as our inspiration, in this paper we present a logic of action, which we call ST, that captures the clear ontological distinction between being responsible for the achievement of a state of affairs and being responsible for the performance of an action. We argue that a relativised modal logic of type RT founded upon a ternary relation over possible worlds integrated with a basic tense logic captures intuitions of the Hamblinian model of imperatives. The logic implements a direct mapping of each of Hamblin’s key concepts: strategies, partial strategies and wholehearted satisfaction.     

The Relevant Equivalence Property

The pure implicational and the multiplicative fragments of arange of propositional relevant (and other) logics are shownto have the property that any two formulas equivalent in sucha logic are constructed from exactly the same propositionalvariables – as opposed to merely having (as the definitionof relevance itself would require) some propositional variablein common.     

Cogency in Motion: Critical Contextualism and Relevance

If arguments are to generate public knowledge, as in the sciences, then they must travel, finding acceptance across a range of local contexts. But not all good arguments travel, whereas some bad arguments do. Under what conditions may we regard the capacity of an argument to travel as a sign of its cogency or public merits? This question is especially interesting for a contextualist approach that wants to remain critically robust: if standards of cogency are bound to local contexts of evaluation, then how may arguments legitimately travel at all? The key to a contextualist conception of cogent travel, I argue, lies in the way local contexts are linked to broader contexts of evaluation by relations of relevance. The burden of the article is to elaborate the different forms these relations can take in the travel of scientific arguments.     

On Vagueness,Truth Values and Fuzzy Logics

Some aspects of vagueness as presented in Shapiro’s book Vagueness in Context [23] are analyzed from the point of fuzzy logic. Presented are some generalizations of Shapiro’s formal apparatus. Presented by Daniele Mundici     

When some is actually all: Scalar inferences in face-threatening contexts

Accounts of the scalar inference from ‘some X-ed’ to ‘not all X-ed’ are central to the debate between contemporary theories of conversational pragmatics. An important contribution to this debate is to identify contexts that decrease the endorsement rate of the inference. We suggest that the inference is endorsed less often in face-threatening contexts, i.e., when X implies a loss of face for the listener. This claim is successfully tested in Experiment 1. Experiment 2 rules out a possible confound between face-threatening contexts and lower-bound contexts. Experiment 3 shows that whilst saying ‘some X-ed’ when one knew for a fact that all X-ed is always perceived as an underinformative utterance, it is also seen as a nice and polite thing to do when X threatens the face of the listener. These findings are considered from the perspective of Relevance Theory as well as that of the Generalized Conversational Inference approach.     

What Does the Frame Problem Tell us About Moral Normativity?

Within cognitive science, mental processing is often construed as computation over mental representations—i.e., as the manipulation and transformation of mental representations in accordance with rules of the kind expressible in the form of a computer program. This foundational approach has encountered a long-standing, persistently recalcitrant, problem often called the frame problem; it is sometimes called the relevance problem. In this paper we describe the frame problem and certain of its apparent morals concerning human cognition, and we argue that these morals have significant import regarding both the nature of moral normativity and the human capacity for mastering moral normativity. The morals of the frame problem bode well, we argue, for the claim that moral normativity is not fully systematizable by exceptionless general principles, and for the correlative claim that such systematizability is not required in order for humans to master moral normativity.

Using logical relevance for question answering

We propose a novel method of determining the appropriateness of an answer to a question through a proof of logical relevance rather than a logical proof of truth. We define logical relevance as the idea that answers should not be considered as absolutely true or false in relation to a question, but should be considered true more flexibly in a sliding scale of aptness. This enables us to reason rigorously about the appropriateness of an answer even in cases where the sources we are getting answers from are incomplete or inconsistent or contain errors. We show how logical relevance can be implemented through the use of measured simplification, a form of constraint relaxation, in order to seek a logical proof than an answer is in fact an answer to a particular question. We then give an example of such an implementation providing a set of specific rules for this purpose.     

Categorical Abstract Algebraic Logic: Prealgebraicity and Protoalgebraicity

Two classes of π are studied whose properties are similar to those of the protoalgebraic deductive systems of Blok and Pigozzi. The first is the class of N-protoalgebraic π-institutions and the second is the wider class of N-prealgebraic π-institutions. Several characterizations are provided. For instance, N-prealgebraic π-institutions are exactly those π-institutions that satisfy monotonicity of the N-Leibniz operator on theory systems and N-protoalgebraic π-institutions those that satisfy monotonicity of the N-Leibniz operator on theory families. Analogs of the correspondence property of Blok and Pigozzi for π-institutions are also introduced and their connections with preand protoalgebraicity are explored. Finally, relations of these two classes with the (, N)-algebraic systems, introduced previously by the author as an analog of the -algebras of Font and Jansana, and with an analog of the Suszko operator of Czelakowski for π-institutions are also investigated. Presented by Josep Maria Font     

Combinatory Logic and the Semantics of Substructural Logics

The results of this paper extend some of the intimate relations that are known to obtain between combinatory logic and certain substructural logics to establish a general characterization theorem that applies to a very broad family of such logics. In particular, I demonstrate that, for every combinator X, if LX is the logic that results by adding the set of types assigned to X (in an appropriate type assignment system, TAS) as axioms to the basic positive relevant logic B∘T, then LX is sound and complete with respect to the class of frames in the Routley-Meyer relational semantics for relevant and substructural logics that meet a first-order condition that corresponds in a very direct way to the structure of the combinator X itself. Presented by Rob Goldblatt