Related papers: Some Remarks on First-Order Definable Tree Languag…
We give a simple new proof that regular languages defined by first-order sentences with no quantifier alteration can be defined by such sentences in which only regular atomic formulas appear. Earlier proofs of this fact relied on arguments…
We study the reactive synthesis problem for distributed systems with an unbounded number of participants interacting with an uncontrollable environment. Executions of those systems are modeled by data words, and specifications are given as…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
This paper presents a complete axiomatization of Monadic Second-Order Logic (MSO) over infinite trees. MSO on infinite trees is a rich system, and its decidability ("Rabin's Tree Theorem") is one of the most powerful known results…
In this paper we define future-time branching temporal logics evaluated over forests, that is, ordered tuples of ordered, but unranked, finite trees. We associate a rich class FL[$\mathcal{L}$] of temporal logics to each set L of (regular)…
We consider the satisfiability problem for the two-variable fragment of first-order logic over finite unranked trees. We work with signatures consisting of some unary predicates and the binary navigational predicates child, right sibling,…
The precise formulation of derivation for tree-adjoining grammars has important ramifications for a wide variety of uses of the formalism, from syntactic analysis to semantic interpretation and statistical language modeling. We argue that…
The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have a definable choice function (by a monadic formula with…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
We propose a new algebraic framework to discuss and classify recognizable tree languages, and to characterize interesting classes of such languages. Our algebraic tool, called preclones, encompasses the classical notion of syntactic…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
A leaf path language is a Boolean combination of sets of the form $\mathsf{{}^mE}^k L$, with $k \ge 1$ and $L$ a regular word language, which consist of those forests where the node labels in at least $k$ leaf-to-root paths make up a word…
Trees -- i.e., the type of data structure known under this name -- are central to many aspects of knowledge organization. We investigate some central design choices concerning the ontological modeling of such trees. In particular, we…
We prove that for a given deterministic top-down transducer with look-ahead it is decidable whether or not its translation is definable (1)~by a linear top-down tree transducer or (2)~by a tree homomorphism. We present algorithms that…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…
We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
I study definable sets in affine continuous logic. Let $T$ be an affine theory. After giving some general results, it is proved that if $T$ has a first order model, its extremal theory is a complete first order theory and first order…
Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…