Related papers: Eine entscheidbare Klasse n-stelliger Horn-Pr\"adi…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…
This paper is a contribution to the study of the universal Horn fragment of predicate fuzzy logics, focusing on the proof of the existence of free models of theories of Horn clauses over Rational Pavelka predicate logic. We define the…
A definite Horn theory is a set of n-dimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be…
This paper tackles the problem of the existence of solutions for recursive systems of Horn clauses with second-order variables interpreted as integer relations, and harnessed by quantifier-free difference bounds arithmetic. We start by…
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…
We study multimodal logics over universally first-order definable classes of frames. We show that even for bimodal logics, there are universal Horn formulas that define set of frames such that the satisfiability problem is undecidable, even…
We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…
We characterise finite axiomatisability and intractability of deciding membership for universal Horn classes generated by finite loop-free hypergraphs.
We prove that the category of models of any relational Horn theory satisfying a mild syntactic condition is infinitely extensive. Central examples of such categories include the categories of preordered sets and partially ordered sets, and…
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
In is paper we present a labelled tableau proof system that serves a wide class of interpretability logics. The system is proved sound and complete for any interpretability logic characterised by a frame condition given by a set of…
We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn…
We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction…
We study word structures of the form $(D,<,P)$ where $D$ is either $\mathbb{N}$ or $\mathbb{Z}$, $<$ is the natural linear ordering on $D$ and $P\subseteq D$ is a predicate on $D$. In particular we show: (a) The set of recursive…
We consider a class of formula equations in first-order logic, Horn formula equations, which are defined by a syntactic restriction on the occurrences of predicate variables. Horn formula equations play an important role in many…
We establish proof-theoretic, constructive and coalgebraic foundations for proof search in coinductive Horn clause theories. Operational semantics of coinductive Horn clause resolution is cast in terms of coinductive uniform proofs; its…
We entirely classify definable sets up to definable bijections in $\mathbb{Z}$-groups, where the language is the one of ordered abelian groups. From this, we deduce, among others, a classification of definable families of bounded definable…
We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC) - a system of higher-order logic modulo theories - and prove its soundness and refutational completeness w.r.t. the standard semantics. As…
We investigate the enumeration of varieties of boolean theories related to Horn clauses. We describe a number of combinatorial equivalences among different characterizations and calculate the number of different theories in $n$ variables…
First-order resolution has been used for type inference for many years, including in Hindley- Milner type inference, type-classes, and constrained data types. Dependent types are a new trend in functional languages. In this paper, we show…