The aim of this paper is the partial axiomatization for firstorder predicate calculus formal system based on first-level universal AND operator. By introducing the universal quantifier and existential quantifier, a predicate calculus formal deductive system ∀ULh∈(0,1] based on 1-level universal AND operator according to propositional calculus formal deductive system ULh∈(0,1] of universal logic...

This paper is concerned with a possible mechanism for learning the meanings of quantifiers in natural language. The meaning of a natural language construction is identified with a procedure for recognizing its extension. Therefore, acquisition of natural language quantifiers is supposed to consist in collecting procedures for computing their denotations. A method for encoding classes of finite ...

Glivenko’s theorem states that an arbitrary propositional formula is classically provable if and only if its double negation is intuitionistically provable. The result does not extend to full first-order predicate logic, but does extend to first-order predicate logic without the universal quantifier. A recent paper by Zdanowski shows that Glivenko’s theorem also holds for secondorder propositio...

Several syntactic and semantic properties of todo N, named bare universal phrase (BUP), and todo(s) o(s) N(s), defined universal phrase (DUP), may be explained by attributing to each quantifier phrase a semantic structure. If our semantic proposal is correct, then Peres’s (1992) claim that the presence of the definite article in the quantifier phrase is vacuous is not right. The semantic struct...

Let I m be the set of subsets of I of cardinality m. Let f be a coloring of I m and g a coloring of I m . We write f → g if every f -homogeneous H ⊆ I is also g-homogeneous. The least m such that f → g for some f : I m → k is called the kwidth of g and denoted by wk(g). In the first part of the paper we prove the existence of colorings with high k-width. In particular, we show that for each k >...

We study an extension of monadic second-order logic of order with the uncountability quantifier “there exist uncountably many sets”. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain monadic second-order logic of order. Additionally we find that the continuum hypothesis holds for classes of sets definable in monadic second-order logic over ...

Hybrid Graph Logic is a logic designed for reasoning about graphs and is built from a basic modal logic, augmented with the use of nominals and a facility to verify the existence of paths in graphs. We study the finite model theory of Hybrid Graph Logic. In particular, we develop pebble games for Hybrid Graph Logic and use these games to exhibit strict infinite hierarchies involving fragments o...

The theory of algebraically closed non-Archimedean valued fields is proved to eliminate quantifiers in an analytic language similar to the one used by Cluckers, Lipshitz and Robinson. The proof makes use of a uniform parameterized normalization theorem which is also proved in this paper and which has far reaching consequences in the geometry of definable sets. This method of proving quantifier ...

The purpose of functional tolerancing process is to define the geometrical specifications of parts ensuring functional requirements. For automotive and aircraft industries, the tolerance synthesis has become an important issue in product design process. Indeed, designers need methods and rules to determine the tolerances. To define rules, a mathematical formulation of tolerance synthesis is det...

1 Introduction Caicedo [1] and others [3] have observed that monadic quantifiers cannot count the number of classes of an equivalence relation. This implies the existence of a binary quantifier which is not definable by monadic quantifiers. The purpose of this paper is to show that binary quantifiers cannot count the dimension of a vector space. Thus we have an example of a ternary quantifier w...