Related papers: Going higher in the First-order Quantifier Alterna…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
Second-order Boolean logic is a generalization of QBF, whose constant alternation fragments are known to be complete for the levels of the exponential time hierarchy. We consider two types of restriction of this logic: 1) restrictions to…
We give an algorithm for the class of second order unification problems in which second order variables have at most one occurrence.
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
Difference Logic (DL) is a fragment of linear arithmetics where atoms are constraints x+k <= y for variables x,y (ranging over Q or Z) and integer k. We study the complexity of deciding the truth of existential DL sentences. This problem…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
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…
We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.
<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…
(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…
We show that for any two distinct words $ s_1, s_2 $ over an arbitrary alphabets, there exists a deterministic finite automaton with $ O(\log^2 n) $ states that accepts $ s_1 $ and rejects $ s_2 $. This improves the previous upper bound of…
This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as…
We establish the strictness of several set quantifier alternation hierarchies that are based on modal logic, evaluated on various classes of finite graphs. This extends to the modal setting a celebrated result of Matz, Schweikardt and…
Recently, the separated fragment (SF) of first-order logic has been introduced. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. SF properly generalizes both the…
We introduce a high-level language with Python-like syntax for string-to-string, polyregular, first-order definable transductions. This language features function calls, boolean variables, and nested for-loops. We devise and implement a…