Logical Pluralism from a Pragmatic Perspective

This paper presents a new view of logical pluralism. This pluralism takes into account how the logical connectives shift, depending on the context in which they occur. Using the Question-Under-Discussion Framework as formulated by Craige Roberts, I identify the contextual factor that is responsible for this shift. I then provide an account of the meanings of the logical connectives which can accommodate this factor. Finally, I suggest that this new pluralism has a certain Carnapian flavour. Questions about the meanings of the connectives or the best logic outside of a specified context are not legitimate questions.     

Proper Semantics for Substructural Logics,from a Stalker Theoretic Point of View

We study filters in residuated structures that are associated with congruence relations (which we call -filters), and develop a semantical theory for general substructural logics based on the notion of primeness for those filters. We first generalize Stone’s sheaf representation theorem to general substructural logics and then define the primeness of -filters as being “points” (or stalkers) of the space, the spectrum, on which the representing sheaf is defined. Prime FL-filters will turn out to coincide with truth sets under various well known semantics for certain substructural logics. We also investigate which structural rules are needed to interpret each connective in terms of prime -filters in the same way as in Kripke or Routley-Meyer semantics. We may consider that the set of the structural rules that each connective needs in this sense reflects the difficulty of giving the meaning of the connective. A surprising discovery is that connectives , ⅋ of linear logic are linearly ordered in terms of the difficulty in this sense. Presented by Wojciech Buszkowski     

The Revival of Rejective Negation

Whether assent (acceptance) and dissent (rejection) are thought of as speech acts or as propositional attitudes, the leading idea of rejectivism is that a grasp of the distinction between them is prior to our understanding of negation as a sentence operator, this operator then being explicable as applying to A to yield something assent to which is tantamount to dissent from A. Widely thought to have been refuted by an argument of Frege"s, rejectivism has undergone something of a revival in recent years, especially in writings by Huw Price and Timothy Smiley. While agreeing that Frege"s argument does not refute the position, we shall air some philosophical qualms about it in Section 5, after a thorough examination of the formal issues in Sections 1–4. This discussion draws on – and seeks to draw attention to – some pertinent work of Kent Bendall in the 1970s.     

Identical Twins,Deduction Theorems,and Pattern Functions: Exploring the Implicative BCSK Fragment of S5

We recapitulate (Section 1) some basic details of the system of implicative BCSK logic, which has two primitive binary implicational connectives, and which can be viewed as a certain fragment of the modal logic S5. From this modal perspective we review (Section 2) some results according to which the pure sublogic in either of these connectives (i.e., each considered without the other) is an exact replica of the material implication fragment of classical propositional logic. In Sections 3 and 5 we show that for the pure logic of one of these implicational connectives two – in general distinct – consequence relations (global and local) definable in the Kripke semantics for modal logic turn out to coincide, though this is not so for the pure logic of the other connective, and that there is an intimate relation between formulas constructed by means of the former connective and the local consequence relation. (Corollary 5.8. This, as we show in an Appendix, is connected to the fact that the ‘propositional operations’ associated with both of our implicational connectives are close to being what R. Quackenbush has called pattern functions.) Between these discussions Section 4 examines some of the replacement-of-equivalents properties of the two connectives, relative to these consequence relations, and Section 6 closes with some observations about the metaphor of identical twins as applied to such pairs of connectives.     

The Acquisition of Temporal Reference Cross-Linguistically Using Two Acting-Out Comprehension Tasks

The acquisition of temporal event referencing, encoded by the temporal connectives: then, before, after, when, while, together, until, and since in English, Thai and Lisu was investigated using two acting-out comprehension tasks, a Marble task and a Toy task. Forty children aged 3.6-7.6 years from each language participated. The Marble and Toy tasks differed in their cognitive complexity: in the Marble task the child had to act out only one clause, whereas in the Toy task the child had to act out both clauses. This task manipulation affected performance in Lisu children only. Language-general effects were found, namely "then" and "together" were relatively early and "since" was relatively late in acquisition. Language-specific effects were found for Thai and Lisu. Results confirm that characteristics of task and test sentences affect children's comprehension of sentences expressing temporal relations and can partially account for the disparity in acquisition order found in previous studies.     

The Pleasures of Anticipation: Enriching Intuitionistic Logic

We explore a relation we call anticipation between formulas, where A anticipates B (according to some logic) just in case B is a consequence (according to that logic, presumed to support some distinguished implicational connective ) of the formula AB. We are especially interested in the case in which the logic is intuitionistic (propositional) logic and are much concerned with an extension of that logic with a new connective, written as a, governed by rules which guarantee that for any formula B, aB is the (logically) strongest formula anticipating B. The investigation of this new logic, which we call ILa, will confront us on several occasions with some of the finer points in the theory of rules and with issues in the philosophy of logic arising from the proposed explication of the existence of a connective (with prescribed logical behaviour) in terms of the conservative extension of a favoured logic by the addition of such a connective. Other points of interest include the provision of a Kripke semantics with respect to which ILa is demonstrably sound, deployed to establish certain unprovability results as well as to forge connections with C. Rauszer's logic of dual intuitionistic negation and dual intuitionistic implication, and the isolation of two relations (between formulas), head-implication and head-linkage, which, though trivial in the setting of classical logic, are of considerable significance in the intuitionistic context.     

Connectives Stranger than Tonk

Many logical systems are such that the addition of Prior's binary connective to them leads to triviality, see [1, 8]. Since is given by some introduction and elimination rules in natural deduction or sequent rules in Gentzen's sequent calculus, the unwanted effects of adding show that some kind of restriction has to be imposed on the acceptable operational inferences rules, in particular if these rules are regarded as definitions of the operations concerned. In this paper, a number of simple observations is made showing that the unwanted phenomenon exemplified by in some logics also occurs in contexts in which is acceptable. In fact, in any non-trivial context, the acceptance of arbitrary introduction rules for logical operations permits operations leading to triviality. Connectives that in all non-trivial contexts lead to triviality will be called non-trivially trivializing connectives.     

Pragmatic connectives,argumentative coherence and relevance

This article is concerned with pragmatic connectives and their uses in discursive argumentation. Three approaches to pragmatic connectives will be presented: (1) argumentation theory, which implies a conception of pragmatics integrated within semantics, and a specific type of argumentative rules, called topoi; (2) discourse structure theory, which associates a function in the structuring of discourse sequences to pragmatic connectives; (3) relevance theory, which constitutes a cognitive pragmatic theory, in which no specific principle is associated to linguistic items. However, two main functions to pragmatic connectives can be proposed: the facilitation of inferences, and the access to relevance. The final purpose of this article is to indicate how argumentative effects in discourse can be explained in a cognitively-based pragmatic theory.     

La fonction argumentative des marques de la langue

The present paper reports a set of experimental studies concerning the comprehension of French argumentative operators and connectives. The first part is a presentation of the theoretical framework, the methodological problems and some of the most general results. Experiments were carried out in the perspective of the linguistic theory of argumentation developed by Anscombre and Ducrot. According to this theory, a number of devices in language are mainly defined by their argumentation function, i.e. by the types of discursive sequences and conclusions they involve. Three categories of such devices were examined: (1) operators like “presque” (almost), “à peine” (hardly), “au moins” (at least), etc. which give an argumentative orientation to the statement; (2) co-orientation connectives, like “même” (even), which relate two statements oriented towards the same conclusion; (3) counter-orientation connectives, like the concessive ones (“mais” (but), “quand même” (even so), etc.), which relate two statements oriented towards opposite conclusions. The data shed light on issues such as: What is the nature of the relationship between the informative and argumentative functions of different operators? Is there a hierarchical relation between the argumentative processes of “co-orientation” and “counter-orientation”? What is the role of negation in the processing of argumentative sequences? The second part of the paper focuses specifically on the study of how 8 and 10 year-old children process “counter-oriented” statements. Five concessive connectives were studied: “mais”, “pourtant”, “quand même”, “même si”, “bien que”. The test was composed of two successive completion tasks: in one task the children had to choose the relevant context of complex sentences involving concessive connectives; in the other task they had to choose their relevant conclusion. Main results show a clear evolution in the performance of children between 8 and 10, suggesting that concessive strategies are not completely mastered at the age of 8. Differences among the concessive connectives studied were brought out: the item “quand même” obtained much better results than the other items with 8-year-old subjects; statements with “mais” seemed to be better processed in the conclusion task than in the context task, especially by 10-year-old subjects. These results are compared with other data obtained in some of the numerous studies on the production and comprehension of concessive connectives in various languages, and discussed from the point of view of argumentative theory.