The quantum logical `or' is analyzed from a physical perspective. We show that it is the existence of EPR-like correlation states for the quantum mechanical entity under consideration that make it nonequivalent to the classical situation. Specifically, the presence of potentiality in these correlation states gives rise to the quantum deviation from the classical logical `or'. We show how this arises not only in the microworld, but also in macroscopic situations where EPR-like correlation states are present. We investigate how application (...) of this analysis to concepts could alleviate some well known problems in cognitive science. (shrink)

In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine these logics in a straightforward way, distributivity holds. On the other hand, distributivity does not arise if we use the usual notion of extension between consequence relations. (...) A detailed discussion about this phenomenon, as well as some possible solutions for it, are given. (shrink)

This study is concerned with the acquisition of the disjunction operator, or, in English. Two mutually inconsistent claims have been made about the acquisition of disjunction. One claim is that the acquisition of the adult truth conditions for logical connectives, including disjunction, is a late and not fully universal, achievement. With particular reference to disjunction, the findings from several studies are interpreted as showing that only the truth conditions associated with exclusive-or are available to young children (e.g., Beilin and Lust (...) 1975; Braine and Rumain 1981, 1983; Paris 1973). There is a related claim, that even when children respond as if they have access to a broader range of truth conditions, namely those associated with inclusive-or, children's adult-like responses are the result of a failure to distinguish or from and (Paris 1973). (shrink)

This paper investigates scalar implicatures and downward entailment in child English. In previous experimental work we have shown that adults’ computation of scalar implicatures is sensitive to entailment relations. For instance, when the disjunction operator or occurs in positive contexts, an implicature of exclusivity arises. By contrast when the disjunction operator occurs within the scope of a downward entailing linguistic expression, no implicature of exclusivity is computed. Investigations on children’s computation of scalar implicatures in the same contexts have led to (...) a slightly different picture. In particular it has proven difficult to demonstrate that children compute scalar implicatures (in non- downward entailing contexts) using the Truth Value Judgment task, a technique that has been used successfully in showing children’s sensitivity to other semantic phenomena. Adopting a different experimental technique called the Felicity Judgment task, however, we demonstrated children’s knowledge of the prerequisites to the computation of scalar implicatures (Chierchia, Crain, Guasti, Gualmini and Meroni, 2001). (shrink)

This paper investigates young children's knowledge of scalar implicatures and downward entailment. In previous experimental work, we have shown that young children access the full range of truth-conditions associated with logical words in classical logic, including the disjunction operator, as well as the indefinite article. The present study extends this research in three ways, taking disjunction as a case study. Experiment 1 draws upon the observation that scalar implicatures (SIs) are cancelled (or reversed) in downward entailing (DE) linguistic environments, e.g., (...) in the scope of negation (Chierchia, 2000). Experiment 2 was designed to determine if scalar implicatures are used by children, like adults, to influence the interpretation of disjunction in non-DE contexts, yielding an implicature of exclusivity for disjunction. Whereas adult controls always rejected assertions of the form A or B in positive (non-DE) contexts in which assertions of the form A and B were also true, many children accepted assertions with disjunction in such contexts. To provide an interpretation to the findings from Experiment 2, a new experimental technique was devised and used in Experiment 3. The new technique presents pairs of assertions to children, who are asked to judge which assertion is a ‘better’ description of the context. The findings from Experiment 3 demonstrated children's awareness that A and B is more informative than A or B in positive contexts, where both statements are true. Taken together, the findings of Experiments 2 and 3 are compatible with the view that some children lack the computational resources to apply scalar implicatures when a single assertion is presented alone (see Reinhart, 1999). (shrink)

This study is concerned with the properties of the disjunction operator, or, and the acquisition of these properties by English-speaking children. Previous research has concluded that adult truth conditions for logical connectives are acquired relatively late in the course of language development. With particular reference to disjunction, the results of several studies have led to two claims. First, it has been argued that the full range of truth-conditions associated with inclusive-or is not initially available to children; instead, children are supposed (...) to interpret disjunction using the truth conditions that are associated with exclusive-or (e.g., Beilin and Lust 1975; Braine and Rumain 1981, 1983; Paris 1973). A second, related claim is that even when children respond as if they have access to the complete range of truth conditions, their responses result from the failure to distinguish or from and (Paris, 1973). (shrink)

Poverty -of-stimulus arguments have taken new ground recently, augmented by experimental findings from th e study of child language. In this paper, we briefly review two variants of the poverty-of-stimulus argument that have received empirical support from studies of child language; then we examine a third argument of this kind in more detail. The case under discussion involves the structural notion of c-command as it pertains to children’s interpretation of disjunction in the scope of negation.

We present a series of arguments for logical nativism, focusing mainly on the meaning of disjunction in human languages. We propose that all human languages are logical in the sense that the meaning of linguistic expressions corresponding to disjunction (e.g. English or , Chinese huozhe, Japanese ka ) conform to the meaning of the logical operator in classical logic, inclusive- or . It is highly implausible, we argue, that children acquire the (logical) meaning of disjunction by observing how adults use (...) disjunction. Findings from studies of child language acquisition and from cross-linguistic research invite the conclusion that children do not learn to be logical—it comes naturally to them. (shrink)

In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. (...) When applied to a certain natural calculus for L, the resulting models are equivalent to a class of abstract logics (in the sense of Brown and Suszko) which we call distributive. Among other results, we prove that D is exactly the class of the algebraic reducts of the reduced models of L, that there is an embedding of the theories of L into the theories of the equational consequence (in the sense of Blok and Pigozzi) relative to D, and that for any algebra A of type (2,2) there is an isomorphism between the D-congruences of A and the models of L over A. In the second part of this paper (which will be published separately) we will also apply some results to give proofs with a logical flavour for several new or well-known lattice-theoretical properties. (shrink)

Two quite simple identities for exclusive disjunction and the biconditional are proven by mathematical induction. This proof is independently reprised in R.E. Jennings' /The Genealogy of Disjunction/ (OUP, 1994) pp. 6-7, esp. p. 7 which points out the consequences for the biconditional of the proof that runs from pages 6-7.

This is a comprehensive study of the English word 'or', and the logical operators variously proposed to present its meaning. Although there are indisputably disjunctive uses of or in English, it is a mistake to suppose that logical disjunction represents its core meaning. 'Or' is descended from the Anglo-Saxon word meaning second, a form which survives in such expressions as "every other day." Its disjunctive uses arise through metalinguistic applications of an intermediate adverbial meaning which is conjunctive rather than disjunctive (...) in character. These conjunctive uses have puzzled philosophers and logicians, and have been discussed extensively under such headings as "free choice permission." This study examines the textbook myths that have clouded our understanding of how or and other "logical" vocabulary comes to have something approaching its logical meaning in natural languages. It considers the various historical conceptions of disjunction and its place in logic from the Stoics to the present day. (shrink)

I argue that the conjunctive distribution of permissibility over or, which is a puzzling feature of free-choice permission is just one instance of a more general class of conjunctive occurrences of the word, and that these conjunctive uses are more directly explicable by the consideration that or is a descendant of oper than by reference to the disjunctive occurrences which logicalist prejudices may tempt us to regard as semantically more fundamental. I offer an account of how the disjunctive uses of (...) or may have come about through an intermediate discourse-adverbial use of or, drawing a parallel with but, which, etymologically, is disjunctive rather than conjunctive and whose conjunctive uses seem to represent just such a discourse-adverbial application. (shrink)

This paper investigates young children's knowledge of scalar implicatures and downward entailment. In previous experimental work, we have shown that young children access the full range of truth-conditions associated with logical words in classical logic, including the disjunction operator, as well as the indefinite article. The present study extends this research in three ways, taking disjunction as a case study. Experiment 1 draws upon the observation that scalar implicatures (SIs) are cancelled (or reversed) in downward entailing (DE) linguistic environments, e.g., (...) in the scope of negation (Chierchia, 2000). Experiment 2 was designed to determine if scalar implicatures are used by children, like adults, to influence the interpretation of disjunction in non-DE contexts, yielding an implicature of exclusivity for disjunction. Whereas adult controls always rejected assertions of the form A or B in positive (non-DE) contexts in which assertions of the form A and B were also true, many children accepted assertions with disjunction in such contexts. To provide an interpretation to the findings from Experiment 2, a new experimental technique was devised and used in Experiment 3. The new technique presents pairs of assertions to children, who are asked to judge which assertion is a ‘better’ description of the context. The findings from Experiment 3 demonstrated children's awareness that A and B is more informative than A or B in positive contexts, where both statements are true. Taken together, the findings of Experiments 2 and 3 are compatible with the view that some children lack the computational resources to apply scalar implicatures when a single assertion is presented alone (see Reinhart, 1999). (shrink)

The connective or can be treated as an inclusive disjunction or else as an exclusive disjunction. Although researchers are aware of this distinction, few have examined the conditions under which each interpretation should be anticipated. Based on linguistic-pragmatic analyses, we assume that interpretations are initially inclusive before either (a) remaining so, or (b) becoming exclusive by way of an implicature ( but not both ). We point to a class of situations that ought to predispose disjunctions to inclusive interpretations and (...) to situations that encourage exclusive interpretations. A disjunction's ultimate interpretation is based on its potential informativeness, where the interpretation of the disjunctive utterance having the smallest number of true conditions is considered most informative. Our investigation leads to five experiments employing arbitrary materials. Among the problems expected to encourage inclusive interpretations are those that present disjunctions in the antecedents of conditionals and in question forms. The best candidates to produce implicatures are those disjunctions that underdetermine an expected conjunctive conclusion, although other disjunctive utterances that are more informative as exclusive are discussed and tested. (shrink)

There is a requirement which a disjunction must satisfy in order to constitute a felicitous contribution to an ordinary conversation: its disjuncts must be interpretable as relevant alternatives. When such an interpretation is not available, the disjunction is highly anomalous. The disjuncts of sentence (1), for example, appear unrelated to one another, and the disjunction is concomitantly odd. The effect is similar when the disjuncts are related but do not constitute distinct alternatives, perhaps by virtue of one disjunct entailing another, (...) as in (2). (shrink)

Mandy Simons. On The Felicity Conditions of Disjunctive Sentences.

Hurford’s Constraint (Hurford, Foundations of Language, 11, 409–411, 1974) states that a disjunction is infelicitous if its disjuncts stand in an entailment relation: #John was born in Paris or in France. Gazdar (Pragmatics, Academic Press, NY, 1979) observed that scalar implicatures can obviate the constraint. For instance, sentences of the form (A or B) or (Both Aand B) are felicitous due to the exclusivity implicature of the first disjunct: A or B implicates ‘not (A and B)’. Chierchia, Fox, and Spector (...) (Handbook of semantics, 2008) use the obviation of Hurford’s Constraint in these cases to argue for a theory of local implicature. I present evidence indicating that the constraint needs to be modified in two ways. First, implicatures can obviate Hurford’s Constraint only in earlier disjuncts, not later ones: #(Both A and B) or (A or B). Second, the constraint rules out not only disjuncts that stand in an entailment relation, but also disjuncts that are even mutually consistent: #John is from Russia or Asia. I propose to make sense of these facts by providing an incremental evaluation procedure which checks that each new disjunct to the right is inconsistent with the information to its left, before the disjunct can be strengthened by local implicature. (shrink)

In this paper Grice’s requirements for assertability are imposed on the disjunction of Classical Logic. Defining material implication in terms of negation and disjunction supplemented by assertability conditions, results in the disappearance of the most important paradoxes of material implication. The resulting consequence relation displays a very strong resemblance to Schurz’s conclusion-relevant consequence relation.

This paper is a contribution to the program of constructing formal representations of pragmatic aspects of human reasoning. We propose a formalization within the framework of Adaptive Logics of the exclusivity implicature governing the connective ‘or’.Keywords: exclusivity implicature, Adaptive Logics.