An algebraic semantics, based on factor algebras, for one-way and two-way implicative verbs is proposed. Implicative verbs denote elements of filters or of ideals generated by identity functions in factor algebras. This semantics explains in particular the problem of implicational equivalence raised by two-way implicative verbs, and shows that the negation necessary to establish the implicativity of these verbs is the negation which preserves the presuppositions of sentences with implicative verbs. In addition, it follows from the proposed semantics that any (...) two implicative verbs denoting in the same algebra but belonging to different categories, are semantically related. (shrink)

The article studies two related issues. First, it introduces the notion of the contraposition of quantifiers which is a “dual” notion of symmetry and has similar relations to co-intersectivity as symmetry has to intersectivity. Second, it shows how symmetry and contraposition can be generalised to higher order type quantifiers, while preserving their relations with other notions from generalized quantifiers theory.

Quanti cateurs Q1 et Q2 du type <1> sont faiblement indépendants si et seulement si Q1Q2(R) = Q2Q1(R1) pour toute relation- produit R. On donne une condition suf sante et nécessaire pour que deux quanti cateurs soient faiblement indépendants.

A simple model accounting for semantic properties of propositional attitude operators in negative contexts with no reference to possible worlds is proposed. Verbs occurring in such operators denote relations between individuals and specific sets of sentences (of a given natural language) and their negation is defined as the complement within a specific set of cognitively determined sentences. This approach avoids in particular the problem of intensionality of propositional attitude operators and allows to use many tools from the generalised quantifier theory. (...) In that way the negation giving rise to factive presuppositions and to the neg-raising is defined in a natural way. (shrink)

A definition of an analytic, a contradictory and a generic sentence, based on the notion of presupposition, is proposed. A sentence is analytic iff it presupposes itself, is contradictory iff it presupposes its own negation, and is generic iff its presuppositions are analytic. A difference is made between an analytic and a necessarily true sentence, and between a contradictory and a necessarily false sentence. There are sentences which are both analytic and contradictory- they are never true and never false. Analytic (...) sentences can have non-trivial consequences, but they are not asserted but presupposed. This fact permits to avoid some classical difficulties with the definition of analytic sentences. A paralleHsm between analytic and generic sentences is indicated. (shrink)

The notion of anaphoric conservativity, that is a property of specific functions taking sets and binary relations as arguments is studied. Such functions are denotations of anaphoric determiners forming nominal anaphors. It is shown that anaphoric conservativity is strictly stronger that ordinary conservativity of this type of functions. In consequence some novel semantic descriptions of reflexive and reciprocal pronouns are provided and a semantic universal stating that reflexive and reciprocal non-possessive determiners denote anaphorically conservative functions is proposed.

We provide necessary and sufficient conditions determining how monotonicity of some classes of reducible quantifiers depends on the monotonicity of simpler quantifiers of iterations to which they are equivalent.

A type quantifier F is symmetric iff F ( X, X )( Y ) = F ( Y, Y )( X ). It is shown that quantifiers denoted by irreducible binary determiners in natural languages are both conservative and symmetric and not only conservative.

It is shown that the notion of the partition of a set can be used to describe in a uniform way the meaning of the expression the same, in its basic uses in transitive and ditransitive sentences. Some formal properties of the function denoted by the same, which follow from such a description are indicated. These properties indicate similarities and differences between functions denoted by the same and generalised quantifiers.

I was first taken to Mr Gurdjieff's flat at a time very different from the present. Paris during the war, under German occupation, was in the grip of the ...