Towards Ranking Geometric Automated Theorem Provers

The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other areas by the strong connection between the axiomatic theories and its standard models. In many cases the geometric constructions are used to establish the theorems' statements, geometric constructions are, in some provers, used to conduct the proof, used as counter-examples to close some branches of the automatic proof. Synthetic geometry proofs are done using geometric properties, proofs that can have a visual counterpart in the supporting geometric construction. With the growing use of geometry automatic deduction tools as applications in other areas, e.g. in education, the need to evaluate them, using different criteria, is felt. Establishing a ranking among geometric automated theorem provers will be useful for the improvement of the current methods/implementations. Improvements could concern wider scope, better efficiency, proof readability and proof reliability. To achieve the goal of being able to compare geometric automated theorem provers a common test bench is needed: a common language to describe the geometric problems; a comprehensive repository of geometric problems and a set of quality measures.Comment: In Proceedings ThEdu'18, arXiv:1903.1240

A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

A Theory Explains Deep Learning

This is our journal for developing Deduction Theory and studying Deep Learning and Artificial intelligence. Deduction Theory is a Theory of Deducing World’s Relativity by Information Coupling and Asymmetry. We focus on information processing, see intelligence as an information structure that relatively close object-oriented, probability-oriented, unsupervised learning, relativity information processing and massive automated information processing. We see deep learning and machine learning as an attempt to make all types of information processing relatively close to probability information processing. We will discuss about how to understand Deep Learning and Artificial intelligence and why Deep Learning is shown better performance than the other methods by metaphysical logic

Bounded Rationality and Heuristics in Humans and in Artificial Cognitive Systems

In this paper I will present an analysis of the impact that the notion of “bounded rationality”, introduced by Herbert Simon in his book “Administrative Behavior”, produced in the field of Artificial Intelligence (AI). In particular, by focusing on the field of Automated Decision Making (ADM), I will show how the introduction of the cognitive dimension into the study of choice of a rational (natural) agent, indirectly determined - in the AI field - the development of a line of research aiming at the realisation of artificial systems whose decisions are based on the adoption of powerful shortcut strategies (known as heuristics) based on “satisficing” - i.e. non optimal - solutions to problem solving. I will show how the “heuristic approach” to problem solving allowed, in AI, to face problems of combinatorial complexity in real-life situations and still represents an important strategy for the design and implementation of intelligent systems

Joint Video and Text Parsing for Understanding Events and Answering Queries

We propose a framework for parsing video and text jointly for understanding events and answering user queries. Our framework produces a parse graph that represents the compositional structures of spatial information (objects and scenes), temporal information (actions and events) and causal information (causalities between events and fluents) in the video and text. The knowledge representation of our framework is based on a spatial-temporal-causal And-Or graph (S/T/C-AOG), which jointly models possible hierarchical compositions of objects, scenes and events as well as their interactions and mutual contexts, and specifies the prior probabilistic distribution of the parse graphs. We present a probabilistic generative model for joint parsing that captures the relations between the input video/text, their corresponding parse graphs and the joint parse graph. Based on the probabilistic model, we propose a joint parsing system consisting of three modules: video parsing, text parsing and joint inference. Video parsing and text parsing produce two parse graphs from the input video and text respectively. The joint inference module produces a joint parse graph by performing matching, deduction and revision on the video and text parse graphs. The proposed framework has the following objectives: Firstly, we aim at deep semantic parsing of video and text that goes beyond the traditional bag-of-words approaches; Secondly, we perform parsing and reasoning across the spatial, temporal and causal dimensions based on the joint S/T/C-AOG representation; Thirdly, we show that deep joint parsing facilitates subsequent applications such as generating narrative text descriptions and answering queries in the forms of who, what, when, where and why. We empirically evaluated our system based on comparison against ground-truth as well as accuracy of query answering and obtained satisfactory results

Benchmarks of programming languages for special purposes in the space station

Although Ada is likely to be chosen as the principal programming language for the Space Station, certain needs, such as expert systems and robotics, may be better developed in special languages. The languages, LISP and Prolog, are studied and some benchmarks derived. The mathematical foundations for these languages are reviewed. Likely areas of the space station are sought out where automation and robotics might be applicable. Benchmarks are designed which are functional, mathematical, relational, and expert in nature. The coding will depend on the particular versions of the languages which become available for testing