Related papers: A Graph Calculus for Predicate Logic
Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of…
We extend the closed graph theorem and the open mapping theorem to a context in which a natural duality interchanges their extensions.
What is ergonomic syntax for relations? In this first paper in a series of two, to answer the question we define regular calculi: a suitably structured functor from a category representing the syntax of regular logic to the category of…
We describe a new method of finding interpolants for classical logic using certain refutation system as a starting point. Refutation can be thought of as an alternative approach to the analysis of formal systems: instead of focusing on…
We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present…
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…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
We propose the use of hyperedge replacement graph grammars for factor graphs, or factor graph grammars (FGGs) for short. FGGs generate sets of factor graphs and can describe a more general class of models than plate notation, dynamic…
Many language technology applications would benefit from the ability to represent negation and its scope on top of widely-used linguistic resources. In this paper, we investigate the possibility of obtaining a first-order logic…
Argument graphs provide an abstract representation of an argumentative situation. A bipolar argument graph is a directed graph where each node denotes an argument, and each arc denotes the influence of one argument on another. Here we…
We add strong negation $N$ to classical logic and interpret the attack relation of "$x$ attacks $y$" in argumentation as $(x\to Ny)$. We write a corresponding object level (using $N$ only) classical theory for each argumentation network and…
In this note, we give a linear-size translation from formulas of first-order logic into equations of the calculus of relations preserving validity and finite validity. Our translation also gives a linear-size conservative reduction from…
In this paper, author uses set theory to construct a logic model of abstract figure from binary relation. Based on the uniform quantified structure, author gives two logic system for graph traversal and graph coloring respectively, moreover…
We show the functional completeness for the connectives of the non-trivial negation inconsistent logic C by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that C contains a strong negation,…
Explaining why an answer is (or is not) returned by a query is important for many applications including auditing, debugging data and queries, and answering hypothetical questions about data. In this work, we present the first practical…
The relational data model requires a theory of relations in which tuples are not only many-sorted, but can also have indexes that are not necessarily numerical. In this paper we develop such a theory and define operations on relations that…
We extend the concept of the law of a finite graph to graphings, which are, in general, infinite graphs whose vertices are equipped with the structure of a probability space. By doing this, we obtain a vast array of new unimodular measures.…
Comparability graphs are a popular class of graphs. We introduce as the digraph analogue of comparability graphs the class of comparability digraphs. We show that many concepts such as implication classes and the knotting graph for a…
Program logics typically reason about an over-approximation of program behaviour to prove the absence of bugs. Recently, program logics have been proposed that instead prove the presence of bugs by means of under-approximate reasoning,…
The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…