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daviddoret authored Aug 27, 2023
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2 changes: 1 addition & 1 deletion docs/build/.buildinfo
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# Sphinx build info version 1
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
config: 7f2341602339f5787e05519e6e1924b2
config: 32dd555d207fe9d43466c601a4446270
tags: 645f666f9bcd5a90fca523b33c5a78b7
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2 changes: 1 addition & 1 deletion docs/build/_sources/bibliography.rst.txt
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************

.. bibliography:: bibliography_bibtex.bib
:style: plain
:cited:
2 changes: 2 additions & 0 deletions docs/build/_sources/disjunction_elimination.rst.txt
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disjunction-elimination
=========================
2 changes: 1 addition & 1 deletion docs/build/_sources/elimination_rule.rst.txt
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Expand Up @@ -7,7 +7,7 @@ Definition
An *introduction-rule* is an :doc:`inference_rule` that allows to derive a formula-statement of some syntactic form from some define premises.

List of well-known *introduction-rules*
--------------------------------------
------------------------------------------

* :doc:`biconditional_elimination_left`
* :doc:`biconditional_elimination_right`
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3 changes: 3 additions & 0 deletions docs/build/_sources/formula_statement.rst.txt
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formula-statement
===================

3 changes: 3 additions & 0 deletions docs/build/_sources/hypothesis.rst.txt
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hypothesis
============

38 changes: 38 additions & 0 deletions docs/build/_sources/inconsistency_introduction_1.rst.txt
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inconsistency-introduction-1
========================================

Definition
----------

*inconsistency-introduction-1* is the :doc:`inference_rule`:

.. math::
\left( P, \neg \left(P\right) \right) \vdash Inc\left(\mathcal{T}\right)
In straightforward language, if we prove a proposition and its negation, it follows that the theory is inconsistent.

Quotes
------

Python sample usage
----------------------

.. admonition:: Source code
:class: tip, dropdown

.. literalinclude :: ../../sample/code/inconsistency_introduction_1.py
:language: python
:linenos:
.. admonition:: Unicode output
:class: note, dropdown

.. literalinclude :: ../../sample/output/inconsistency_introduction_1_unicode.txt
:language: text
.. admonition:: Plaintext output
:class: note, dropdown

.. literalinclude :: ../../sample/output/inconsistency_introduction_1_plaintext.txt
:language: text
41 changes: 41 additions & 0 deletions docs/build/_sources/inconsistency_introduction_2.rst.txt
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inconsistency-introduction-2
========================================

Definition
----------

*inconsistency-introduction-2* is the :doc:`inference_rule`:

.. math::
\left(\left(x = y\right), \left(x \neq y\right)\right) \vdash Inc\left(\mathcal{T}\right)
In straightforward language, if we prove both the equality and inequality of two terms, it follows that the theory is inconsistent.

Quotes
----------

A proof of consistency will have to show, by appealing to contentual considerations which are completely unproblematic, that in the formalism in question it is never possible to derive the formula 𝑎 ≠ 𝑎, or alternatively it is not possible to prove both 𝑎 = 𝑏 and 𝑎 ≠ 𝑏. :cite:p:`mancosu_2021_introductionprooftheorynormalization{p. 5}`


Python sample usage
----------------------

.. admonition:: Source code
:class: tip, dropdown

.. literalinclude :: ../../sample/code/inconsistency_introduction_2.py
:language: python
:linenos:
.. admonition:: Unicode output
:class: note, dropdown

.. literalinclude :: ../../sample/output/inconsistency_introduction_2_unicode.txt
:language: text
.. admonition:: Plaintext output
:class: note, dropdown

.. literalinclude :: ../../sample/output/inconsistency_introduction_2_plaintext.txt
:language: text
41 changes: 41 additions & 0 deletions docs/build/_sources/inconsistency_introduction_3.rst.txt
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inconsistency-introduction-3
========================================

Definition
----------

*inconsistency-introduction-3* is the :doc:`inference_rule`:

.. math::
\left( P \neq P \right) \vdash Inc\left(\mathcal{T}\right)
In straightforward language, if we prove that an object is not equal to itself, it follows that the theory is inconsistent.

Quotes
----------

A proof of consistency will have to show, by appealing to contentual considerations which are completely unproblematic, that in the formalism in question it is never possible to derive the formula 𝑎 ≠ 𝑎, or alternatively it is not possible to prove both 𝑎 = 𝑏 and 𝑎 ≠ 𝑏. :cite:p:`mancosu_2021_introductionprooftheorynormalization{p. 5}`


Python sample usage
----------------------

.. admonition:: Source code
:class: tip, dropdown

.. literalinclude :: ../../sample/code/inconsistency_introduction_3.py
:language: python
:linenos:
.. admonition:: Unicode output
:class: note, dropdown

.. literalinclude :: ../../sample/output/inconsistency_introduction_3_unicode.txt
:language: text
.. admonition:: Plaintext output
:class: note, dropdown

.. literalinclude :: ../../sample/output/inconsistency_introduction_3_plaintext.txt
:language: text
16 changes: 15 additions & 1 deletion docs/build/_sources/index.rst.txt
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Expand Up @@ -13,24 +13,38 @@ Welcome to punctilious's documentation!
:maxdepth: 1
:caption: Contents:

test

absorption
bibliography
biconditional_elimination_left
biconditional_elimination_right
biconditional_introduction
conjunction_elimination_left
conjunction_elimination_right
conjunction_introduction
disjunction_elimination
disjunction_introduction_left
disjunction_introduction_right
double_negation_elimination
double_negation_introduction
elimination_rule
inconsistency_by_inequality_introduction
formula_statement
hypothesis
inconsistency_introduction_1
inconsistency_introduction_2
inconsistency_introduction_3
inference_rule
introduction_rule
is_a
meta_object
modus_ponens
notation_form
paragraph_proof
proof_by_contradiction_1
proof_by_contradiction_2
proof_by_refutation_1
proof_by_refutation_2
relation
theory_elaboration_sequence
universe_of_discourse
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2 changes: 1 addition & 1 deletion docs/build/_sources/introduction_rule.rst.txt
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Expand Up @@ -7,7 +7,7 @@ Definition
An *introduction-rule* is an :doc:`inference_rule` that allows to derive a formula-statement of some syntactic form from some define premises.

List of well-known *introduction-rules*
--------------------------------------
-----------------------------------------

* :doc:`biconditional_introduction`
* :doc:`conjunction_introduction`
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35 changes: 35 additions & 0 deletions docs/build/_sources/proof_by_contradiction_1.rst.txt
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proof-by-contradiction-1
=========================

Definition
-----------

*proof-by-contradiction-1* is the :doc:`inference_rule`:

.. math::
\left( \mathcal{H} assume \not \mathbf{P}, Inc\left(\mathcal{H}\right) \right) \vdash \mathbf{P}
Python implementation
----------------------

Sample usage
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. literalinclude :: ../../sample/code/proof_by_contradiction_1.py
:language: python
.. literalinclude :: ../../sample/output/proof_by_contradiction_1_unicode.txt
:language: text
Documentation
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. module:: core
:noindex:
.. autoclass:: InferenceRuleInclusionDict
:members: proof_by_contradiction_1

Bibliography
------------

.. footbibliography::
35 changes: 35 additions & 0 deletions docs/build/_sources/proof_by_contradiction_2.rst.txt
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proof-by-contradiction-2
=========================

Definition
----------

*proof-by-contradiction-2* is the :doc:`inference_rule`:

.. math::
\left( \mathcal{H} assume \not \mathbf{P}, Inc\left(\mathcal{H}\right) \right) \vdash \mathbf{P}
Python implementation
---------------------

ProofByContradiction2Declaration
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. module:: core
:noindex:
.. autoclass:: ProofByContradiction2Declaration
:members:
:special-members: __init__

ProofByContradiction2Inclusion
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. autoclass:: ProofByContradiction2Inclusion
:members:
:special-members: __init__

Bibliography
------------

.. footbibliography::
41 changes: 41 additions & 0 deletions docs/build/_sources/proof_by_refutation_1.rst.txt
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proof-by-refutation-1
=========================

Definition
----------

*proof-by-refutation-1* is the :doc:`inference_rule`:

.. math::
\left( \boldsymbol{\mathcal{H}} \: \textit{assume} \: \neg \boldsymbol{P}, \boldsymbol{P}, Inc\left( \boldsymbol{\mathcal{H}} \right) \right) \vdash \boldsymbol{P}
Where:
* :math:`\boldsymbol{\mathcal{H}}` is an :doc:`hypothesis`
* :math:`\boldsymbol{P}` is a :doc:`formula_statement`

In plain language, it consists in posing the hypothesis that a proposition :math:`\boldsymbol{P}` is not true, refuting that hypothesis by proving :math:`\boldsymbol{P}`, inferring the inconsistency of that hypothesis from this contradiction, and finally inferring :math:`\boldsymbol{P}`.

Python implementation
---------------------

ProofByRefutation1Declaration
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. module:: core
:noindex:
.. autoclass:: ProofByRefutation1Declaration
:members:
:special-members: __init__

ProofByRefutation1Inclusion
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. autoclass:: ProofByRefutation1Inclusion
:members:
:special-members: __init__

Bibliography
------------

.. footbibliography::
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proof-by-refutation-2
=========================

Definition
----------

*proof-by-refutation-2* is the :doc:`inference_rule`:

.. math::
\left( \mathcal{H} assume \not \mathbf{P}, Inc\left(\mathcal{H}\right) \right) \vdash \mathbf{P}
Python implementation
---------------------

ProofByRefutation2Declaration
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. module:: core
:noindex:
.. autoclass:: ProofByRefutation2Declaration
:members:
:special-members: __init__

ProofByRefutation2Inclusion
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. autoclass:: ProofByRefutation2Inclusion
:members:
:special-members: __init__

Bibliography
------------

.. footbibliography::
5 changes: 5 additions & 0 deletions docs/build/_sources/test.rst.txt
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minimalist example
=====================

.. literalinclude :: ../../sample/output/proof_by_contradiction_1_unicode.txt
:language: text
11 changes: 11 additions & 0 deletions docs/build/_static/css/custom.css
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/*
Fix to assure text wrapping in code and code output inclusions implemented with the literalinclude sphinx directive.
References:
- https://docs.readthedocs.io/en/stable/guides/adding-custom-css.html
- https://stackoverflow.com/questions/66971299/sphinx-documentation-with-readthedocs-theme-text-block-wrapping
- https://stackoverflow.com/questions/46800045/how-to-wrap-a-long-literal-block-in-restructuredtext
*/
pre {
white-space: pre-wrap !important;
word-break: break-all;
}
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