Related papers: Quantifier-free formulas and quantifier alternatio…
We describe the layer of quantifier alternation depth at most one of the quantifier completion of a Boolean doctrine over a small category. This amounts to a doctrinal version of Herbrand's theorem for formulas with quantifier alternation…
We introduce a novel decidable fragment of first-order logic. The fragment is one-dimensional in the sense that quantification is limited to applications of blocks of existential (universal) quantifiers such that at most one variable…
Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the…
The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough…
We present the first complete axiomatisation for quantifier-free separation logic. The logic is equipped with the standard concrete heaplet semantics and the proof system has no external feature such as nominals/labels. It is not possible…
Quantified modal logic provides a natural logical language for reasoning about modal attitudes even while retaining the richness of quantification for referring to predicates over domains. But then most fragments of the logic are…
The issue of non-perturbative background independent quantization of matrix models is addressed. The analysis is carried out by considering a simple matrix model which is a matrix extension of ordinary mechanics reduced to 0 dimension. It…
Uniform one-dimensional fragment UF1^= is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
<p>We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted…
Quantifier elimination (QE) and Craig interpolation (CI) are central to various state-of-the-art automated approaches to hardware and software verification. They are rooted in the Boolean setting and are successful for, e.g., first-order…
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment of first-order logic to contexts involving relations of arity greater than two. Quantifiers in this…
The problem is the classification of the ideals of ``free differential algebras", or the associated quotient algebras, the q-algebras; being finitely generated, unital C-algebras with homogeneous relations and a q-differential structure.…
Let $\alpha\geq 2$ be any ordinal. We consider the class $\mathsf{Drs}_{\alpha}$ of relativized diagonal free set algebras of dimension $\alpha$. With same technique, we prove several important results concerning this class. Among these…
The Stratified Foundations are a restriction of naive set theory where the comprehension scheme is restricted to stratifiable propositions. It is known that this theory is consistent and that proofs strongly normalize in this theory.…
We show that every finite Boolean combination of polynomial equalities and inequalities in C^n admits two uniform normal forms: an $\exists\forall$ form and a $\forall\exists$ form, each using a single polynomial equation. Both forms use…
Quantified Boolean formulas (QBFs) generalize propositional formulas by admitting quantifications over propositional variables. QBFs can be viewed as (restricted) formulas of first-order predicate logic and easy translations of QBFs into…
Stratified formulae were introduced by Quine as an alternative way to attack Russell's Paradox. Instead of limiting comprehension by size (as in $\mathsf{ZF}$ set theory, using its axiom scheme of separation), unlimited comprehension is…
Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the…
We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the…