Slides - Association for Logic in India

Formal Definitions Of
Reason Fallacies To
Aid Defect
Exploration In
Argument Gaming
G.S. Mahalakshmi, Lecturer, Anna University, Chennai – 25
mahalakshmi@cs.annauniv.edu, gs_maha@yahoo.co.in
Walton’s definition of Fallacy
A
fallacy is
an argument (or at least something that
purports to be an argument);
 that falls short of some standard of
correctness;
 poses a serious obstacle to the realization of
the goal of a dialogue.

 For
Walton, a fallacy is fundamentally
negative; it involves a lapse, error,
failure, and deception.
Argument Gaming

knowledge sharing - exchange of ideas to promote learning - method
of interaction – argument gaming

subject of discussion validated – with right justifications and by
eliminating false beliefs


False beliefs – proposed in arguments (which support the argument) - need
to be identified

Reasons support subject of discussion in argument – false reasons - Reason
fallacies

To identify reason fallacies or defects or holes is reasoning from argumentation
Indian philosophical perspective – ‘tarka’ methodology

Motivation – invariable concomitance

knowledge of co-existence free from fallacious knowledge

Applied when convincing others of a certain issue

When the sun is at the top, vertically over your head, you infer that the time is around 12.00 noon.

When a student answers ‘Penguins fly’, the teacher infers the student’s lack of knowledge about ‘Penguin’
Interpretation of arguments in

‘This hill has fire’ (statement)


‘Because it has smoke’ (reason)


Lake – subject; fire – probandum or object to be inferred
‘Because it has smoke’ (reason)


Oven – similar example
This lake has fire’ (statement)


Smoke – probans or Reason
‘Since whatever has smoke has fire e.g. an oven’ (example)


Hill – subject; fire – probandum or object to be inferred
Smoke – probans or Reason
‘Since whatever has smoke has fire e.g. an oven’ (example)

Oven – similar example

May not be a smoke, it may be ‘fog’, so statement is
disproved
Need for exploration of reason
fallacies

Modern argumentation

Argument fallacies

How an argument is put forth, rather than its NL
semantic content



Argument by expert opinion, straw man fallacy etc.
No rule framed – surveyed and studied only by examples
Conceptual Semantic analysis – needed
Identifying abstract semantics by using relations between
concepts that form the argument
 By exploring relations between parts of argument –
concepts (probans, probandum, subject)



Invariable concomitance, inherence, causal, contact-contact
etc.
Possibility of rules – standards inspired by Tarka Sastra
Nyaya - Argument Defects
Defective Reasoning - 5
 tells how (or how not) to interpret a proposition
 a subject, which prevents inferential knowledge
Definitions of defects

Straying


Adverse


concept to which the subject is related to is not present or not
related as said, with the subject
Stultified


Two valid reasons for presence and absence of the thing to be
proved
Unestablished


Reason is pervaded by negation of the thing to be proved
Antithetical


Reason which is present in a place where there is absence of the
thing to be proved
Negation of probandum is established by another proof
Need for defect categorisation


Concept and relation centric
would provide more information about reason fallacies present in
the proposed argument
Formal definitions of defects
……
…….
Our idea – categories of Nyaya
defects
Defect Table - Possible defects classified per
defect category
Defect classification,
identification
Nyaya
Defect
types
Argument
Analysis
Defect
Categories
Defect Table
Defect set
Sample arguments
Arg.
Id
Argument
Subject
object of
inference
reason
1
sky_lotus has fragrance
sky_lotus
fragrance
Nil
2
artificial-rose has fragrance
artificialfragrance
rose
Nil
3
lily has fragrance
lily
fragrance
Nil
4
mountain has fire due_to smoke
mountain
fire
smoke
5
penguin fly because it is-a bird
penguin
fly
Bird
6
bats are viviparous because they are mammal
bat
viviparous
mammal
7
Falls does not have fire when there is smoke
falls
fire
smoke
8
Falls does not have fire when there is smoke
falls
fire
smoke
Argument defects
Arg.
Id
1
Status in KB
Defect Category & Type
Status in KB
concept doesn't exists
HC1
Unestablished to subject
concept doesn't exists
HC7
Unestablished to itself
concept exists,
quality(negation)
2
concept exists,
quality(negation)
3
concept and quality exists
No Defect
concept and quality exists
4
Fire, smoke exists as concepts. No
invariable relation
HC8
Unestablished to invariance
Fire, smoke exists as concepts. No
invariable relation
5
Penguin and bird exists as concept.
Exclusive quality: fly in negation
HC4
Straying Uncommon
Penguin and bird exists as concept.
Exclusive quality: fly in negation
6
Bat, mammal and bird exist as
concept. Mammal-viviparous, bird~viviparous
HC2, HC5
Antithetical
Bat, mammal and bird exist as
concept. Mammal-viviparous, bird~viviparous
7
Falls and smoke exist as concept.
Absence of fire as concept. Direct
relation between fire and smoke
HC1, HC5
Straying Common
Falls and smoke exist as concept.
Absence of fire as concept. Direct
relation between fire and smoke
HC1, HC6
Falls and smoke exist as concept.
Absence of fire as concept. Invariable
8
fragrance
as
a
Falls and smoke exist as concept.
Absence of fire as concept. Invariable
fragrance
as
a
Future enhancements
 Other
provisional definitions of
invariable concomitance
 More Reason fallacies in Buddhist
philosophy
 Coverage of argument fallacies
Key References
1.
Gautama, The Nyaya Sutras, translated by S.C. Vidyabhusana, edited by
Nanda Lal Sinha, Sacred Book of the Hindus, Allahabad, (1930). Reprinted in
1990. Delhi: Motilal Banarsidass
2.
C. L. Hamblin. Fallacies. London:Methuen, (1970).
3.
Jaakko Hintikka, Socratic Epistemology: Explorations of Knowledge-Seeking
by Questioning, Cambridge University Press, 239pp., (2007)
4.
G.S.Mahalakshmi and T.V.Geetha: Navya-Nyaya Approach to Defect
Exploration in Argument Gaming for Knowledge Sharing, In proc. of
International Conf. on Logic, Navya-Nyaya & Applications - A Homage To
Bimal Krishna Matilal (ICLNNA ‘07), Jadavpur Univ., Calcutta, India, (2007).
5.
Sathis Chandra Vidyabhusana, A History of Indian Logic – Ancient,
Medieaeval and Modern Schools, Motilal Banarsidass Publishers Private Ltd.,
Delhi, India, ISBN:81-208-0565-8. pp. 84, (1988).
6.
Swami Virupakshananda: Tarka Samgraha, Sri Ramakrishna Math, Madras
(1994).
7.
Toshihiro Wada, Invariable Concomitance in Navya-Nyaya, Sri Garib Dass
Oriental Series No. 101, Indological and Oriental Publishers, New Delhi,
India, (1990).
8.
Walton, D. and Woods, J., Argument: The Logic of the fallacies, Toronto:
Thank You…
Gautama –
Ontology editor
based on Nyaya
G.S. Mahalakshmi, Lecturer, Anna University, Chennai – 25
mahalakshmi@cs.annauniv.edu, gs_maha@yahoo.co.in
Idea

Indian logic based approach of knowledge representation


classifies the world knowledge into concepts, and relations, both
enriched with special qualities.
Nyaya Sastra



Nyaya logics



categorization of world knowledge
elaborate in tapping the minute details in the defined knowledge units.
mechanism which defines the concept and relation elements of ontology
based on the epistemology of Nyaya-Vaisheshika school of Indian logic.
NORM



an ontology reference model based on Nyaya logic
syntax and semantics of NORM rdf.
To overcome the difficulty involved


we propose Gautama,
Gautama

a tool for editing the ontology based on Nyaya logics.
Nyaya Logics - Argument
A=<
Aid,
CS,COI,CR,RS-OI,RS-R,RR-OI,Astate,Astatus,Astr>
Aid - Argument index
CS,COI,CR - concept categories;
RS-OI,RS-R,RR-OI - relation categories;
Astate – state of argument;
Astate {premise, inference, conclusion}
Astatus – defeat status of arguments;
Astatus{defeated, undefeated, ambiguous, undetermined}
NORM Model
(a)
(b)
(c)
ontology with concepts as nodes and
external relations as edges
a concept with qualities as nodes, internal
relations as thin edges, tangential relations
as dotted edges
a quality with values as nodes, grouping
relations as edges
NORM - Concept
C= <Cname, Ccat, QM,QO,QE,Cpr,Cpar,Ccon>
Cname – name of the concept
Ccat={CS,COI,CR}
QM = Quality Mandatory of type Quality Q
QO = Quality optional of type Quality Q
QE = Quality Exceptional of type Quality Q
Cpr = Concept priority weight factor
Cpar= parent concept C, par = 0 to n;
n – max. no. of concepts in committed ontology
Ccon = constraint set under which concept C is said to exist;
NORM - Quality
Q=<Qname,Vi,Qcon>
Qname – name of the quality
Vi – Quality value list;
i = 0 to v, max. no. of values allowed for Qname
Qcon – constraint set of Qname
Nyaya-Vaisheshika Qualities
NORM - Relation
R= <Rname,CAq,CBq,Rcat,Rqual,Rpr,Rcon> Rname – name of the relation
CAq, CBq ⊆ Ccat ;
q = 1 to n; n – max. no. of qualities defined for CA, CB in OT;
CA = CB permissible.
Rcat={RS-OI,RS-R,RR-OI}
Rqual={Ici,D,X,Xp},
Ic – Invariable concomitance; i = 0-3, over {sym, +Ic, -Ic, Neutral}; D – Direct;
X – Exclusive; Xp - Exceptional
Rpr = Relation priority weight factor
Rcon = constraint set over defined relations, {Rcon[i], R1, R2}; R1, R2 ∈ R.
i=0, reflexive, here R1, R2 = NULL ; i=1,
‘Gautama’ tool
Gautama - Description
ILO Visualisation Pane:


Concepts Visualisation Pane:


only the concept hierarchy in the ontology is visualised.
Nodes Entry Pane:


provides controls for entering information about the nodes that are yet to be created


C-C denotes concept-concept; V-V denotes value-value and Q-Q denotes quality-quality.
command buttons provided to add concepts, qualities and values.

‘Generate RDF’ button helps in generation of Resource description format
Relations Entry Pane:


‘roles’ shall be created - at all levels as per NORM

command buttons for ‘deletion’ services.

‘load rdf’ button to load a pre-defined ontology at once.
Concepts list Pane:


contains icons to save and print the ontology visualisation created in the top left pane of the
editor. In addition, drawing icons have also been provided.

lists all the concepts

specialised concepts first , followed by the generalised concepts.
Quality List Pane:
NORM RDF

<rdf:concept>


<rdf:name>


used to declare the role of a concept / quality
<rdf:category>


used to declare the type of a concept / quality / relation
<rdf:role>


used to create member qualities for a given concept
<rdf:type>


used to create concept axioms
<rdf:quality>


used to create descriptions or definitions for a particular concept
<rdf:axiom>


used to declare the name of a concept / quality / relation.
<rdf:desc>


used to declare a concept prior and after its definition
used to declare the category of relation like external, internal, tangential or
grouping.
<rdf:operator>

used to declare the logical operators like and, or while creating the concept
NDL

Concept-satisfiable


Concept-subsumes


This command has three variations. It either checks whether a concept is related
to another concept, through a particular relation name or through a particular set
of relation categories.
Chk-quality


These commands retrieve the child nodes or parent nodes of the parametric
concept from the ontology hierarchy
Chk-concept-related


These commands list the ancestral / descending concepts in the ontology
hierarchy. Role-ancestors and Role-descendants also have similar purpose.
Sub-concept, Super-concept


This takes two concepts as input, and checks whether the first concept subsumes
the second concept. This is one of the famous reasoning service provided by any
ontology-based reasoner.
Concept ancestors and Concept-descendants


This takes a concept name as the parameter and checks whether the addition of
the concept will not violate the ontology definitions that exist prior to the
execution of this command
This command checks the entire ontology hierarchy to check if the required quality
is available in the ontology
Chk-concept-quality

This command checks the entire ontology hierarchy to check if the particular
concept has the required quality.
Future enhancements
 Translation
of NORM RDF into visualised
ontology in Gautama
 Improving visualisation
 Color coding for qualities and relations
across levels
 Merging
two IL ontologies
 Automated IL ontology creation from
text passages
Key References

G. Aghila, G.S. Mahalakshmi and Dr. T.V. Geetha, ‘KRIL – A
Knowledge Representation System based on Nyaya Shastra using
Extended Description Logics’, VIVEK journal, ISSN 0970-1618, Vol.
15, No.3, pp. 3-18, July (2003).

Gautama, The Nyaya Sutras, translated by S.C. Vidyabhusana,
edited by Nanda Lal Sinha, Sacred Book of the Hindus, Allahabad,
(1930). Reprinted in 1990. Delhi: Motilal Banarsidass

Jonardon Ganeri, Indian Logic: A Reader, Published by Routledge,
(2001)

G.S. Mahalakshmi and T.V. Geetha, Reasoning and Evolution of
consistent ontologies using NORM, IJAI, Indian Society for
Development and Environment Research (ISDER), ISSN 0974-0635,
Volume 2, Number S09, pp. 77-94, Spring (2009).

Swami Virupakshananda, Tarka Samgraha, Sri Ramakrishna Math,
Madras, (1994).
Thank You…