1,261 research outputs found
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
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Towards Informed Exploration for Deep Reinforcement Learning
In this thesis, we discuss various techniques for improving exploration for deep reinforcement learning. We begin with a brief review of reinforcement learning (RL) and the fundamental v.s. exploitation trade-off. Then we review how deep RL has improved upon classical and summarize six categories of the latest exploration methods for deep RL, in the order increasing usage of prior information. We then explore representative works in three categories discuss their strengths and weaknesses. The first category, represented by Soft Q-learning, uses regularization to encourage exploration. The second category, represented by count-based via hashing, maps states to hash codes for counting and assigns higher exploration to less-encountered states. The third category utilizes hierarchy and is represented by modular architecture for RL agents to play StarCraft II. Finally, we conclude that exploration by prior knowledge is a promising research direction and suggest topics of potentially impact
Automated sequence and motion planning for robotic spatial extrusion of 3D trusses
While robotic spatial extrusion has demonstrated a new and efficient means to
fabricate 3D truss structures in architectural scale, a major challenge remains
in automatically planning extrusion sequence and robotic motion for trusses
with unconstrained topologies. This paper presents the first attempt in the
field to rigorously formulate the extrusion sequence and motion planning (SAMP)
problem, using a CSP encoding. Furthermore, this research proposes a new
hierarchical planning framework to solve the extrusion SAMP problems that
usually have a long planning horizon and 3D configuration complexity. By
decoupling sequence and motion planning, the planning framework is able to
efficiently solve the extrusion sequence, end-effector poses, joint
configurations, and transition trajectories for spatial trusses with
nonstandard topologies. This paper also presents the first detailed computation
data to reveal the runtime bottleneck on solving SAMP problems, which provides
insight and comparing baseline for future algorithmic development. Together
with the algorithmic results, this paper also presents an open-source and
modularized software implementation called Choreo that is machine-agnostic. To
demonstrate the power of this algorithmic framework, three case studies,
including real fabrication and simulation results, are presented.Comment: 24 pages, 16 figure
Description logics of context
We introduce Description Logics of Context (DLCs)—an extension of Description Logics (DLs) for context-based reasoning. Our approach descends from J. McCarthy's tradition of treating contexts as formal objects over which one can quantify and express first-order properties. DLCs are founded in two-dimensional possible world semantics, where one dimension represents a usual object domain and the other a domain of contexts, and accommodate two interacting DL languages—the object and the context language—interpreted over their respective domains. Effectively, DLCs comprise a family of two-sorted , two-dimensional combinations of pairs of DLs. We argue that this setup ensures a well-grounded, generic framework for capturing and studying mechanisms of contextualization in the DL paradigm. As the main technical contribution, we prove 2ExpTime-completeness of the satisfiability problem in the maximally expressive DLC, based on the DL forumla . As an interesting corollary, we show that under certain conditions this result holds also for a range of two-dimensional DLs, including the prominent forumla
An interval logic for higher-level temporal reasoning
Prior work explored temporal logics, based on classical modal logics, as a framework for specifying and reasoning about concurrent programs, distributed systems, and communications protocols, and reported on efforts using temporal reasoning primitives to express very high level abstract requirements that a program or system is to satisfy. Based on experience with those primitives, this report describes an Interval Logic that is more suitable for expressing such higher level temporal properties. The report provides a formal semantics for the Interval Logic, and several examples of its use. A description of decision procedures for the logic is also included
Abductive Equivalential Translation and its application to Natural Language Database Interfacing
The thesis describes a logical formalization of natural-language database
interfacing. We assume the existence of a ``natural language engine'' capable
of mediating between surface linguistic string and their representations as
``literal'' logical forms: the focus of interest will be the question of
relating ``literal'' logical forms to representations in terms of primitives
meaningful to the underlying database engine. We begin by describing the nature
of the problem, and show how a variety of interface functionalities can be
considered as instances of a type of formal inference task which we call
``Abductive Equivalential Translation'' (AET); functionalities which can be
reduced to this form include answering questions, responding to commands,
reasoning about the completeness of answers, answering meta-questions of type
``Do you know...'', and generating assertions and questions. In each case, a
``linguistic domain theory'' (LDT) and an input formula are given,
and the goal is to construct a formula with certain properties which is
equivalent to , given and a set of permitted assumptions. If the
LDT is of a certain specified type, whose formulas are either conditional
equivalences or Horn-clauses, we show that the AET problem can be reduced to a
goal-directed inference method. We present an abstract description of this
method, and sketch its realization in Prolog. The relationship between AET and
several problems previously discussed in the literature is discussed. In
particular, we show how AET can provide a simple and elegant solution to the
so-called ``Doctor on Board'' problem, and in effect allows a
``relativization'' of the Closed World Assumption. The ideas in the thesis have
all been implemented concretely within the SRI CLARE project, using a real
projects and payments database. The LDT for the example database is described
in detail, and examples of the types of functionality that can be achieved
within the example domain are presented.Comment: 162 pages, Latex source, PhD thesis (U Stockholm, 1993). Uses
style-file ustockholm_thesis.st
Capturing proof process
PhD ThesisProof automation is a common bottleneck for industrial adoption of formal methods.
Heuristic search techniques fail to discharge every proof obligation (PO), and
significant effort is spent on proving the remaining ones interactively. Luckily,
they usually fall into several proof families, where a single idea is required to discharge
all similar POs. However, interactive formal proof requires expertise and
is expensive: repeating the ideas over multiple proofs adds up to significant costs.
The AI4FM research project aims to alleviate the repetitive effort by “learning”
from an expert doing interactive proof. The expert’s proof attempts can give rise
to reusable strategies, which capture the ideas necessary to discharge similar POs.
Automatic replay of these strategies would complete the remaining proof tasks
within the same family, enabling the expert to focus on novel proof ideas.
This thesis presents an architecture to capture the expert’s proof ideas as a highlevel
proof process. Expert insight is not reflected in low-level proof scripts, therefore
a generic ProofProcess framework is developed to capture high-level proof information,
such as proof intent and important proof features of the proof steps taken.
The framework accommodates branching to represent the actual proof structure
as well as layers of abstraction to accommodate different granularities. The full
history of how the proof was discovered is recorded, including multiple attempts
to capture alternative, failed or unfinished versions.
A prototype implementation of the ProofProcess framework is available, including
integrations with Isabelle and Z/EVES theorem provers. Two case studies illustrate
how the ProofProcess systems are used to capture high-level proof processes
in examples from industrial-style formal developments. Reuse of the captured
information to discharge similar proofs within the examples is also explored.
The captured high-level information facilitates extraction of reusable proof
strategies. Furthermore, the data could be used for proof maintenance, training,
proof metrics, and other use cases
lim+, delta+, and Non-Permutability of beta-Steps
Using a human-oriented formal example proof of the (lim+) theorem, i.e. that
the sum of limits is the limit of the sum, which is of value for reference on
its own, we exhibit a non-permutability of beta-steps and delta+-steps
(according to Smullyan's classification), which is not visible with
non-liberalized delta-rules and not serious with further liberalized
delta-rules, such as the delta++-rule. Besides a careful presentation of the
search for a proof of (lim+) with several pedagogical intentions, the main
subject is to explain why the order of beta-steps plays such a practically
important role in some calculi.Comment: ii + 36 page
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