Related papers: Proof-graphs for Minimal Implicational Logic
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Most interesting proofs in mathematics contain an inductive argument which requires an extension of the LK-calculus to formalize. The most commonly used calculi for induction contain a separate rule or axiom which reduces the valid proof…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
Handsome proof nets were introduced by Retor\'e as a syntax for multiplicative linear logic. These proof nets are defined by means of cographs (graphs representing formulas) equipped with a vertices partition satisfying simple topological…
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…
A semantic tableau method, called an argumentation tableau, that enables the derivation of arguments, is proposed. First, the derivation of arguments for standard propositional and predicate logic is addressed. Next, an extension that…
Knowledge graph reasoning is the fundamental component to support machine learning applications such as information extraction, information retrieval, and recommendation. Since knowledge graphs can be viewed as the discrete symbolic…
Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative…
Deep inference is a proof theoretic methodology that generalizes the standard notion of inference of the sequent calculus, whereby inference rules become applicable at any depth inside logical expressions. Deep inference provides more…
The aim of this thesis is to present an extension to the string graphs of Dixon, Duncan and Kissinger that allows the finite representation of certain infinite families of graphs and graph rewrite rules, and to demonstrate that a logic can…
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 of which instances…
Diagrammatic, analogical or iconic representations are often contrasted with linguistic or logical representations, in which the shape of the symbols is arbitrary. The aim of this paper is to make a case for the usefulness of diagrams in…
This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units…
We introduce a graphical refutation calculus for relational inclusions: it reduces establishing a relational inclusion to establishing that a graph constructed from it has empty extension. This sound and complete calculus is conceptually…
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of…
The present paper is the first one in the sequence of papers about a simple class of {\em framed $4$-graphs}; the goal of the present paper is to collect some well-known results on planarity and to reformulate them in the language of {\em…
We introduce a method to find network motifs in knowledge graphs. Network motifs are useful patterns or meaningful subunits of the graph that recur frequently. We extend the common definition of a network motif to coincide with a basic…
Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is…