Mathematics flagship (preliminar)

Mathematics flagship


Mathematical Grammar Library

Contributors: Jordi Saludes, Ares Ribó, Sebastian Xambó, Olga Caprotti, Aarne Ranta, Krasimir Angelov, Ramona Enach, Adam Slaski, Thomas Hallgren, Shafqat Mumtaz Virk

.notes: Contributors for Fre, Rus?


Cloud services for mathematics


Multilingual semantic wiki


Features


Example

Wiki translations


Multi-modal input/output of mathematics

.notes: This is also shown in the Query technologies flagship


Interfacing Sage


Sage interface workflow

Sage workflow


Word problem solver dialog system


Workflow

workflow


Word problem schemata

The current prototype allows to state word problems of the following form:


Setting the problem model

We considered two levels of discourse:

The fact that John has seven fruit is represented by the GF tree:

fromProp (E1owns john (gen Fruit n7))

and in Prolog by:

own(john, 7 * fruit)

while in core, it converts to the Prolog assertion:

p(X, fruit, own(john, X)) - 7 * unit(fruit)).

The latter is more suited to reasoning with it.


Normalization

Conjunctions are disaggregated: namely

is converted into:

Questions make the unknown explicit in the core expressions:

is represented in plain as:

find(own(mary,apple))

and in core as:

find(X, apple, own(mary,X))  

Example

% abs:fromProp (E1owns john (gen Fruit n7))
% Eng:John has seven fruit .
p(X, fruit, own(john, X)) - 7 * unit(fruit).

% abs:fromProp (E1owns john (aplus (ConsAmount (gen Apple n2) 
%              (BaseAmount (some Orange) (gen Banana n3)))))
% Eng:John has two apples , some oranges and three bananas .
p(Y, apple, own(john, Y)) - 2 * unit(apple).
p(Z, banana, own(john, Z)) - 3 * unit(banana).
p(V, orange, own(john, V)) - some(orange).

% abs:fromQuestion (Q1owns john Orange)
% Eng:how many oranges does John have ?
find(W, orange, own(john, W)).

Solving a problem

To process a given word problem, the student must construct a set of of statements in core language that model that given word problem.

The authoring interpreter saves a word problem in a Prolog file consisting of:


Modeling a problem

When the dialog interpreter is started on a word problem file, the system uses the GF abstract lines to display the statement of the problem in the selected language.

Next, the student must go through a sequence of steps to have the problem correctly modeled by:

  1. assigning variables to given data and to unknowns

  2. discovering relations among the given data

  3. stating equations involving these unknowns


Steps 1 and 2


Steps 3 and 4

AttachmentSize
sage-wf.pdf28.17 KB
wproblems-wf.pdf54.2 KB
wiki-translations.png34.37 KB