Differences

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--- sav08:propositional_logic_semantics [2008/03/11 14:49]
vkuncak
+++ sav08:propositional_logic_semantics [2008/03/11 14:51]
vkuncak
@@ Line 14: / Line 14: @@
 \[\begin{array}{l}
   e(p)(I) = I(p), \mbox{ for } p \in V \\
-  e({"\lnot"}\> F)(I) = \lnot (e(F)(I)) \\
+  e({"\lnot "}\> F)(I) = \lnot (e(F)(I)) \\
-  e(F_1\> {"\land"}\> F_2)(I) = e(F_1)(I) \land e(F_2)(I) \\
+  e(F_1\> {"\land "}\> F_2)(I) = e(F_1)(I) \land e(F_2)(I) \\
-  e(F_1\> {"\lor"}\> F_2)(I) = e(F_1)(I) \lor e(F_2)(I) \\
+  e(F_1\> {"\lor "}\> F_2)(I) = e(F_1)(I) \lor e(F_2)(I) \\
-  e(F_1\> {"\rightarrow"}\> F_2)(I) = (e(F_1)(I) \rightarrow e(F_2)(I)) \\
+  e(F_1\> {"\rightarrow "}\> F_2)(I) = (e(F_1)(I) \rightarrow e(F_2)(I)) \\
-  e(F_1\> {"\leftrightarrow"}\> F_2)(I) = (e(F_1)(I) \leftrightarrow e(F_2)(I))
+  e(F_1\> {"\leftrightarrow "}\> F_2)(I) = (e(F_1)(I) \leftrightarrow e(F_2)(I))
-\end{array}\]
+\end{array}
-We wrote symbols like $"\land"$ on left in quotes to emphasize that those are syntactic entities, in contrast to symbols like $\land$ on right-hand side that denote propositional operations given by truth tables (stated in [[Propositional Logic Informally]]).
+\]
+We wrote symbols like $" \land "$ on left in quotes to emphasize that those are syntactic entities, in contrast to symbols like $\land$ on right-hand side that denote propositional operations given by truth tables (stated in [[Propositional Logic Informally]]).
 ++++
 This definition follows one in the formula evaluator in [[homework01]].