Semantic entailment.html (1256B)
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="created" content="2018-02-13 14:40:36 +0000"/><meta name="updated" content="2018-03-27 15:53:19 +0000"/><title>Semantic entailment</title></head><body><div>ϕ₁, …, ϕ<span style="vertical-align: sub;">n </span>⊨<span style="vertical-align: sub;" />Ψ</div><div><br/></div><div>A formula Ψ is semantically entailed by premises (ϕ₁, …, ϕ<span style="vertical-align: sub;">n</span>) if every valuation that makes premises true makes Ψ true.</div><div><br/></div><div>counterexample makes premises true but not conclusion</div><div><br/></div><div>if ϕ ⊨ Ψ and Ψ ⊨ ϕ, ϕ ≡ Ψ </div><div><img src="Semantic%20entailment.resources/screenshot.png" height="203" width="825"/><br/></div><div><img src="Semantic%20entailment.resources/screenshot_1.png" height="236" width="824"/><br/></div><div><br/></div></body></html>