Related papers: Global Numerical Constraints on Trees
We determine the complexity of counting models of bounded size of specifications expressed in Linear-time Temporal Logic. Counting word models is #P-complete, if the bound is given in unary, and as hard as counting accepting runs of…
Standard Description Logics (DLs) can encode quantitative aspects of an application domain through either number restrictions, which constrain the number of individuals that are in a certain relationship with an individual, or concrete…
One-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential (universal) quantifiers that leave at most one variable free. We investigate this fragment over words and trees, presenting a…
Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information which instances…
Knowledge representation and reasoning in law are essential to facilitate the automation of legal analysis and decision-making tasks. In this paper, we propose a new approach based on legal science, specifically legal taxonomy, for…
Dependency syntax represents the structure of a sentence as a tree composed of dependencies, i.e., directed relations between lexical units. While in its more general form any such tree is allowed, in practice many are not plausible or are…
Given a logic presented in a sequent calculus, a natural question is that of equivalence of proofs: to determine whether two given proofs are equated by any denotational semantics, ie any categorical interpretation of the logic compatible…
We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded…
Algorithmic meta-theorems state that problems definable in a fixed logic can be solved efficiently on structures with certain properties. An example is Courcelle's Theorem, which states that all problems expressible in monadic second-order…
We study alternating register automata on data words and data trees in relation to logics. A data word (resp. data tree) is a word (resp. tree) whose every position carries a label from a finite alphabet and a data value from an infinite…
The tree based representation described in this paper, hereditarily binary numbers, applies recursively a run-length compression mechanism that enables computations limited by the structural complexity of their operands rather than by their…
The paper proposes a theoretical approach of the debugging of constraint programs based on a notion of explanation tree. The proposed approach is an attempt to adapt algorithmic debugging to constraint programming. In this theoretical…
Linear tree constraints were introduced by Hofmann and Rodriguez in the context of amortized resource analysis for object oriented programs. More precisely, they gave a reduction from inference of resource types to constraint solving. Thus,…
Two results are presented concerning the entailment problem in Separation Logic with inductively defined predicate symbols and theory reasoning. First, we show that the entailment problem is undecidable for rules with bounded tree-width, if…
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…
The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.
So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky's work). However, some linguistic phenomena do not cope properly…
We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
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…