We present several calculi that integrate equality handling by superposition and ordered paramodulation into a free variable tableau calculus. We prove completeness of this calculus by an adaptation of themodel generation [1, 13] technique commonly used for completeness proofs of resolution calculi. The calculi and the completeness proof are compared to earlier results of Degtyarev and Voronkov...

A formula (x) in the one non-logical symbol " with one free variable x is Russell if the sentence :9r8x(x"r $ (x)) is logically valid. This note describes a pattern common to the classical examples of Russell formulas, adds a couple of new ones, and constructs many formulas that are near-Russell.

Language 2 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 λ-calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

We study the semantics of SPARQL queries with optional matching features under entailment regimes. We argue that the normative semantics may lead to answers that are in conflict with the intuitive meaning of optional matching, where unbound variables naturally represent unknown information. We propose an extension of the SPARQL algebra that addresses these issues and is compatible with any enta...

Inference rule substitution of equals for equals has been formalized in terms of simple substitution which performs a replacement even though a free occurrence of a variable is captured contextual substitution which prevents such capture and func tion application We show that in connection with pure rst order predicate calculus the function application and no capture versions of the inference r...

In a recently published paper J. C. C. McKinsey has pointed out some difficulties which arise from Axiom I of my theory of probability implication. This axiom states the unambiguity of the degree p of a given probability implication (03VP) for the case that the class 0 is not empty, a condition formulated by (o), but postulates ambiguity of p in case of an empty class 0, this condition being fo...

The goal of dependence logic is to establish a basic theory of dependence and independence underlying such seemingly unrelated subjects as causality, random variables, bound variables in logic, database theory, the theory of social choice, and even quantum physics. There is an avalanche of new results in this field demonstrating remarkable convergence. The concepts of (in)dependence in the diff...

Where do linguistic forms come from? Researchers have proposed accounts based on rules, conventions, constraints, statistical regularities, discourse patterns, language contact, neurology, physical dynamics and genes. What is common to all of these forces is that they must all make their final impact at the moment of speaking. Some of these forces operate within a narrow time frame. For example...

Optimal robust MPC for constrained linear systems that are subject to additive uncertainty requires a closed loop optimization with computation that rises exponentially with the prediction horizon, N . This was overcome by parameterized tube MPC (PTMPC) that used a triangular separable prediction strategy in which predictions are decomposed into a nominal and N − 1 partial prediction sequences,...

One of the fundamental and seemingly simple aims of mathematical knowledge management (MKM) is to develop and standardize formats that allow to “represent the meaning of the objects of mathematics”. The open formats OpenMath and MathML address this, but differ subtly in syntax, rigor, and structural viewpoints (notably over calculus). To avoid fragmentation and smooth out interoperability obsta...