How to translate When in propositional logic? The suggestions given are fine, but there is not always a direct read over from natural language to formal logic: when could mean "whenever" but there could, in natural language, be an implied "only" as "I only buy food when I get paid" and that is just one of the slippery ambiguities which formal language is explicitly designed to avoid
What is the logical operator for but? - Mathematics Stack Exchange An alternative way of conveying the same information would be to say "I am fine and he has flu " Often, the word but is used in English to mean and, especially when there is some contrast or conflict between the statements being combined To determine the logical form of a statement you must think about what the statement means, rather than just translating word by word into symbols
Whats the difference between predicate and propositional logic? Propositional logic is an axiomatization of Boolean logic As such predicate logic includes propositional logic Both systems are known to be consistent, e g by exhibiting models in which the axioms are satisfied Propositional logic is decidable, for example by the method of truth tables: [Truth table -- Wikipedia] and "complete" in that every tautology in the sentential calculus (basically
Associativity of logical connectives - Mathematics Stack Exchange According to the precedence of logical connectives, operator $\\rightarrow$ gets higher precedence than $\\leftrightarrow$ operator But what about associativity of $\\rightarrow$ operator? The implies
Definition of identity law in the laws of proposition I'm sure this is an easy one but I'm struggling From my notes, there's this example on how to simplify a proposition using proposition laws: p $\\lor$ (p$\\land$ q) $\\equiv$ (p $\\land$ t) $\\lor
What is the logical connective for Either. . Or? [duplicate] I have a statement, Either p or q and I have to write it in terms of logical connectives but I don't get which logical connector should I be using? Here is what I did (I think there could have be
What does the notation $\\Gamma \\vDash \\phi$ mean (in Mathematical . . . In yet other words, $\phi$ is true in every model of $\Gamma$ If we're not speaking about ordinary first-order logic, something else may take the place of "structure" above -- for example, for propositional calculus, instead of $\forall\mathfrak A$ we would quantify over all truth assignments for the propositional variables in $\Gamma$ and $\phi$
Propositional Logic- Resolution Rule - Mathematics Stack Exchange I'm currently taking an Artificial Intelligence class and we recently covered the topic of logical agents This is the solution to a question asked about using the resolution inference algorithm: