Related papers: Horn Clauses in Hybrid-Dynamic First-Order Logic
The uniform one-dimensional fragment of first-order logic, U1, is a formalism that extends two-variable logic in a natural way to contexts with relations of all arities. We survey properties of U1 and investigate its relationship to…
Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages…
Given a sequence $\{\Pi_n\}$ of Horn logic programs, the limit $\Pi$ of $\{\Pi_n\}$ is the set of the clauses such that every clause in $\Pi$ belongs to almost every $\Pi_n$ and every clause in infinitely many $\Pi_n$'s belongs to $\Pi$…
In quantum information and computation research, symbolic methods have been widely used for human specification and reasoning about quantum states and operations. At the same time, they are essential for ensuring the scalability and…
This reports introduces a novel sound and complete semantics for first order intuitionistic logic, in the framework of category theory and by the computational interpretation of the logic based on the so-called Curry-Howard isomorphism.…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and…
Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations,…
Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
Formally specifying, let alone verifying, properties of systems involving multiple programming languages is inherently challenging. We introduce Heterogeneous Dynamic Logic (HDL), a framework for combining reasoning principles from distinct…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of…
First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…
Deductive verification of hybrid systems (HSs) increasingly attracts more attention in recent years because of its power and scalability, where a powerful specification logic for HSs is the cornerstone. Often, HSs are naturally modelled by…
We study the problem of rewriting an ontology O1 expressed in a DL L1 into an ontology O2 in a Horn DL L2 such that O1 and O2 are equisatisfiable when extended with an arbitrary dataset. Ontologies that admit such rewritings are amenable to…
We introduce the logic FOCN(P) which extends first-order logic by counting and by numerical predicates from a set P, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature. We…
An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…
Application domains that require considering relationships among objects which have real-valued attributes are becoming even more important. In this paper we propose NeuralLog, a first-order logic language that is compiled to a neural…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…