Computational Aristotelian Logic - Part 2 of 3
In addition to input propositions, choose the rules of the game!
Klaus Glashoff's Homepage
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Contact
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Aim of this site
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Short Introduction
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Remarks on notation
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References and links
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Exercises
Step 1:
Insert Input-propositions:
Step 2:
Choose Syllogisms (press Ctrl for multiple choice)
/* Example:*/ A(x,y) A(y,z) I(u,v) Ouz Evt Ayw
Figure 1
Barbara
Celarent
Darii
Ferio
Barbari
Celaront
Syllog.rules:
Axy,Ayz->Axz
Axy,Eyz->Exz
Ixy,Ayz->Ixz
Ixy,Eyz->Oxz
Axy,Ayz->Ixz
Axy,Eyz->Oxz
Figure 2
Cesare
Camestres
Festino
Baroco
Cesaro
Camestrop
Syllog.rules:
Axy,Ezy->Exz
Exy,Azy->Exz
Ixy,Ezy->Oxz
Oxy,Azy->Oxz
Axy,Ezy->Oxz
Exy,Azy->Oxz
Step 3:
Choose conversion and/or subaltern. rules:
E-con
version: Exy->Eyx
I-con
version: Ixy->Iyx
A-sub
alternation: Axy->Ixy
E-sub
alternation: Exy->Oxy
A-pcon
version: Axy->Iyx
E-pcon
version: Exy->Oyx
Figure 3
Darapti
Disamis
Datisi
Felapton
Bocardo
Ferison
Syllog.rules:
Ayx,Ayz->Ixz
Ayx,Iyz->Ixz
Iyx,Ayz->Ixz
Ayx,Eyz->Oxz
Ayx,Oyz->Oxz
Iyx,Eyz->Oxz
Figure 4
Bamalip
Camenes
Dimatis
Fesapo
Fresison
Camenop
Syllog.rules:
Ayx,Azy->Ixz
Eyx,Azy->Exz
Ayx,Izy->Ixz
Ayx,Ezy->Oxz
Iyx,Ezy->Oxz
Eyx,Azy->Oxz
Id
entity: ->Axx for all terms x
Terms x and z
allowed to be
identical
in syllogisms
Step 4:
Example
To Part 1
To Part 3
Input
-sentences are:
Output
-sentences
(Consequences of the Input-sentences):
Protocoll
of syllogistic rules
applied during the derivation:
1: A(x,y)
2: A(y,z)
3: I(u,v)
4: O(u,z)
5: E(v,t)
6: A(y,w)
6: A(y,w)