Symbolic Logic
Exam 1 Review 

Here are some things to be familiar with for the first exam.

• what are predicates, individual constants, and logical connectives? What are the constraints on predicates and constants (e.g. whether a constant can name more than one object, whether an object can fail to have a name, whether a predicate can be vague or ambiguous)? What is the arity of a predicate? What is an atomic sentence?
• what is logical validity? logical equivalence? logical consequence? logical necessity? How are logical equivalence, consequence, and necessity related to tautological equivalence, tautological consequence, and tautology?
• be able to identify sentences as tautologies, logical necessities, Tarski's World necessities, or not necessary at all. (Remember, you can use truth tables to determine whether a sentence is in the first category, and you can determine whether a sentence is in the last category by seeing whether you can construct a Tarski's world that makes it false.)
• logical equivalences: DeMorgan's laws, associativity, commutativity, idempotence, double negation, distribution.

• know truth tables for basic logical connectives, and know how to apply them to construct truth tables for complex sentences.
• know how many rows a truth table must have; know how to construct the base or reference columns (you need to follow the procedure used by our textbook; it's just a convention, and other conventions are possible, but I want to be able to evaluate your truth tables without spending a lot of time figuring out which convention you're using).
• know how to use truth tables to determine whether a sentence is a tautology, whether two sentences are tautologically equivalent, and whether one sentence is a tautological consequence of a set of other sentences.

• know how to translate sentences from English into symbolic notation. (The English sentences will either use English equivalents of Tarski's World predicates, which you should already know how to translate, or I will give you a list of predicates you can use in the translation.)
• You should also know how to translate sentences from symbolic notation into English, but it's not likely I will ask questions like this on the exam.
• Good practice: make sure you can do the translation homework exercises. (If you had trouble with any of them, go back and take another look.)
• Make sure you know how to handle "neither . . . nor" sentences! Also keep in mind that lots of English expressions should get translated as "and," including "but," "however," "nevertheless," etc.

• know how to do proofs using all the rules we have covered so far: =Intro, =Elim, Reit, ∧Intro, ∧Elim, ∨Intro, ∨Elim, ¬Intro,  ¬Elim, ⊥Intro, and ⊥Elim.
• Proofs will resemble the ones you've done for homework. Good practice would be to make sure you can construct proofs corresponding to the DeMorgan's equivalences, and the other logical equivalences we have discussed, for example the distribution equivalences and the associative equivalences. Make sure you can do the homework proofs we have done so far; it might also be helpful to do unassigned homework proofs.