Oct 28, 2020 · $\begingroup$ 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 ...

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]

$\begingroup$ In my lecture notes for a class that deals with logical operators, the following is an exercise: $$$$"Write each...in symbolic logic...": Grumpy has a long nose but Stupy doesn't. Grumpy has a long nose but Stupy doesn't.

May 28, 2016 · I have the following sentences: I won't go the library unless I need a book p: I will go the library q: I need a book I replaced unless with if not as follows: I won't go the library if I don't n...

In simple terms, could someone explain why there is not a logical connective for ‘because’ in propositional logic like there is for ‘and’ and ‘or’? Is this because the equivalent of ‘because’ is the argument of the form ‘if p, then q’, or am I missing something? Please illustrate your answer with example(s) if possible.

Aug 3, 2021 · Propositional Logic Translation. 2. Problem with translating sets into logic. 0. Conceptual difference ...

Propositional Logic - Associative Property question. Ask Question Asked 12 years ago. Modified 12 years ago.

(For example, we can do logic without $\to$ and $\land$ and get an equivalent logical system. Often, we keep redundant symbols, because the axioms become less simple and less self-evident without them.) The most misunderstood element of standard propositional logic is …

May 30, 2015 · Simplifying propositional logic. Ask Question Asked 9 years, 8 months ago. Modified 9 years, 8 months ago.

The latter convention is the case in proof complexity when one is measuring the depth of a formula. If a first-order quantified formula is translated to propositional logic, then $\forall$ will correspond to a conjunction, and $\exists$ to a disjunction; it makes sense not to penalize the formula for the size of the underlying universe.