Universal & Existential quantification.html (1644B)
1 <?xml version="1.0" encoding="UTF-8"?> 2 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> 3 <html><head><link rel="stylesheet" type="text/css" href="sitewide.css"><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/><meta name="exporter-version" content="Evernote Mac 7.0.3 (456341)"/><meta name="keywords" content="logic"/><meta name="altitude" content="-1.32824182510376"/><meta name="author" content="Alex Balgavy"/><meta name="created" content="2018-03-06 15:59:00 +0000"/><meta name="latitude" content="52.33302833890655"/><meta name="longitude" content="4.86553639720129"/><meta name="source" content="desktop.mac"/><meta name="updated" content="2018-03-06 16:15:09 +0000"/><title>Universal & Existential quantification</title></head><body><div><span style="font-weight: bold;">Universal</span></div><div>∀x ϕ — for all values of x, ϕ is true</div><div>∀x x — contradiction</div><div><br/></div><div>in propositional logic:</div><div>∀x ϕ ≡ ϕ<span style="vertical-align: sub;">1</span> ∧ ϕ<span style="vertical-align: sub;">0</span></div><div><br/></div><div><span style="font-weight: bold;">Existential</span></div><div>∃x ϕ — there exists a value of x where ϕ is true</div><div>∃x x — tautology</div><div><br/></div><div>in propositional logic:</div><div>∃x ϕ ≡ ϕ<sub>1</sub> ∨ ϕ<sub>0</sub></div><div><sub><br/></sub></div><div>Build OBDDs using the propositional logic versions. Compute the variables and then take conjunction (∀) or disjunction (∃).</div><div><br/></div><div><br/></div></body></html>