Shifting to a Higher Gear in a Natural Language System

We have completed the development of the REL System, a system for communicating with the computer in natural language concerning a relational database. We have been using that system in a series of experiments on how people actually do communicate in solving an intellectual task. These experiments, together with our general experience with REL, and related work elsewhere, have led us to the specification and development of a new system, the POL (Problem Oriented Language) System. POL is an evolutionary extension of REL, preserving what has worked, and extending and adding new capabilities to meet observed needs. These improvements include more responsive diagnostics, handling of sentence fragments, inter knowledge base communications, and new facilities for building and extending the knowledge bases of users. This paper introduces POL

FormalGeo: An Extensible Formalized Framework for Olympiad Geometric Problem Solving

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.Comment: 44 page

Socially-distributed cognition and cognitive architectures: towards an ACT-R-based cognitive social simulation capability

ACT-R is one of the most widely used cognitive architectures, and it has been used to model hundreds of phenomena described in the cognitive psychology literature. In spite of this, there are relatively few studies that have attempted to apply ACT-R to situations involving social interaction. This is an important omission since the social aspects of cognition have been a growing area of interest in the cognitive science community, and an understanding of the dynamics of collective cognition is of particular importance in many organizational settings. In order to support the computational modeling and simulation of socially-distributed cognitive processes, a simulation capability based on the ACT-R architecture is described. This capability features a number of extensions to the core ACT-R architecture that are intended to support social interaction and collaborative problem solving. The core features of a number of supporting applications and services are also described. These applications/services support the execution, monitoring and analysis of simulation experiments. Finally, a system designed to record human behavioral data in a collective problem-solving task is described. This system is being used to undertake a range of experiments with teams of human subjects, and it will ultimately support the development of high fidelity ACT-R cognitive models. Such models can be used in conjunction with the ACT-R simulation capability to test hypotheses concerning the interaction between cognitive, social and technological factors in tasks involving socially-distributed information processing

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

Memory-Based Lexical Acquisition and Processing

Current approaches to computational lexicology in language technology are knowledge-based (competence-oriented) and try to abstract away from specific formalisms, domains, and applications. This results in severe complexity, acquisition and reusability bottlenecks. As an alternative, we propose a particular performance-oriented approach to Natural Language Processing based on automatic memory-based learning of linguistic (lexical) tasks. The consequences of the approach for computational lexicology are discussed, and the application of the approach on a number of lexical acquisition and disambiguation tasks in phonology, morphology and syntax is described.Comment: 18 page

Multilevel poetry translation as a problem-solving task

Poems are treated by translators as hierarchical multilevel systems. Here we propose the notion of “multilevel poetry translation” to characterize such cases of poetry translation in terms of selection and rebuilding of a multilevel system of constraints across languages. Different levels of a poem correspond to different sets of components that asymmetrically constrain each other (e. g., grammar, lexicon, syntactic construction, prosody, rhythm, typography, etc.). This perspective allows a poem to be approached as a thinking-tool: an “experimental lab” which submits language to unusual conditions and provides a scenario to observe the emergence of new patterns of semiotic behaviour as a result. We describe this operation as a problem-solving task, and exemplify with Augusto de Campos’ Portuguese translation of John Donne’s poem “The Expiration.

POWERPLAY: Training an Increasingly General Problem Solver by Continually Searching for the Simplest Still Unsolvable Problem

Most of computer science focuses on automatically solving given computational problems. I focus on automatically inventing or discovering problems in a way inspired by the playful behavior of animals and humans, to train a more and more general problem solver from scratch in an unsupervised fashion. Consider the infinite set of all computable descriptions of tasks with possibly computable solutions. The novel algorithmic framework POWERPLAY (2011) continually searches the space of possible pairs of new tasks and modifications of the current problem solver, until it finds a more powerful problem solver that provably solves all previously learned tasks plus the new one, while the unmodified predecessor does not. Wow-effects are achieved by continually making previously learned skills more efficient such that they require less time and space. New skills may (partially) re-use previously learned skills. POWERPLAY's search orders candidate pairs of tasks and solver modifications by their conditional computational (time & space) complexity, given the stored experience so far. The new task and its corresponding task-solving skill are those first found and validated. The computational costs of validating new tasks need not grow with task repertoire size. POWERPLAY's ongoing search for novelty keeps breaking the generalization abilities of its present solver. This is related to Goedel's sequence of increasingly powerful formal theories based on adding formerly unprovable statements to the axioms without affecting previously provable theorems. The continually increasing repertoire of problem solving procedures can be exploited by a parallel search for solutions to additional externally posed tasks. POWERPLAY may be viewed as a greedy but practical implementation of basic principles of creativity. A first experimental analysis can be found in separate papers [53,54].Comment: 21 pages, additional connections to previous work, references to first experiments with POWERPLA