The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class a(Dn(Σ2)) for some natural number n ≥ 1, where a is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space 2 into the class ∆2, and the notions of Wadge degree...

The main goal of this paper is to introduce and investigate the related theory on monadic effect algebras. First, we design axiomatic system existential quantifiers algebras then use it give definition universal quantifier Then, relatively complete subalgebra prove that there exists a one-to-one correspondence between set all subalgebras. Moreover, characterize generated formula ideals Riesz co...

The essence of scope in natural language semantics can be characterized as follows: an expression e1 takes scope over an expression e2 iff the interpretation of the former affects the interpretation of the latter. Consider, for example, the sentence in (1) below, which is typical of the cases discussed in this paper in that it involves an indefinite and a universal (or, more generally, a non-ex...

In this survey paper, we present several results linking quantifier-free axiomatizations of various Euclidean and hyperbolic geometries in languages without relation symbols to geometric constructibility theorems. Several fragments of Euclidean and hyperbolic geometries turn out to be naturally occurring only when we ask for the universal theory of the standard plane (Euclidean or hyperbolic), ...

In the paper a first order language is constructed. It includes the universal quantifier and the following propositional connectives: truth, negation, and conjunction. The variables are divided into three kinds: bound variables, fixed variables, and free variables. An infinite number of predicates for each arity is provided. Schemes of structural induction and schemes justifying definitions by ...

This report describes several approaches for handling synthesis conjectures within an Satisfiability Modulo Theories (SMT) solver. We describe approaches that primarily focus on determining the unsatisfiability of the negated form of synthesis conjectures using new techniques for quantifier instantiation. 1 Synthesis in an SMT solver A synthesis conjecture states there exists a function f for w...

We consider proofs in minimal logic, written in natural deduction style. The only rules are introduction and elimination for implication and the universal quantifier. The logical connectives ∃,∧ are seen as special cases of inductively defined predicates, and hence are defined by the introduction and elimination schemes ∀x(A→ ∃xA), ∃xA→ ∀x(A→ B)→ B (x not free in B), A→ B → A ∧B, A ∧B → (A→ B →...

Different quantifier types in Quantified Boolean Formulae (QBF) introduce variable dependencies which have to be taken into consideration when deciding satisfiability of a QBF. In this work, we focus on dependencies based on syntactically connected variables. We generalize our previous ideas for efficiently representing dependency sets of universal variables to existential ones. We obtain a dep...

Motivated by applications to program verification, we study a decision procedure for satisfiability in an expressive fragment of a theory of arrays, which is parameterized by the theories of the array elements. The decision procedure reduces satisfiability of a formula of the fragment to satisfiability of an equisatisfiable quantifier-free formula in the combined theory of equality with uninter...

Programming with assertions constitutes an effective tool to detect and correct programming errors. The ability of executing formal specifications is essential in order to test automatically an implementation against its assertions. However, formal assertions may describe recursive models which are difficult to identify so current assertion checkers limit, in a considerable way, the expressivit...