abductive reasoning al-farabi al-ghazali al-kindi alan turing alfred north whitehead alfred tarski alonzo church analytic proof antinomy argument argumentation theory aristotle automated theorem proving averroes avicenna axiom axiomatic system bertrand russell boolean function boolean satisfiability problem cartesian closed category categorial grammar charles peirce classical logic cogency completeness computability logic consistency critical thinking curry-howard correspondence cut-elimination theorem dag prawitz david hilbert deductive reasoning deductive system deontic logic dharmakirti dialetheism doxastic logic epistemic logic fakhr al-din al-razi fallacy fictionalism finitism first-order logic formal grammar formal interpretation formal language formal proof formal semantics formal system foundations of mathematics fuzzy logic georg cantor george boole gerhard gentzen giuseppe peano gottlob frege hilary putnam history of logic ibn hazm ibn taymiyyah ibn al-nafis indian logic inductive reasoning inference informal logic interactive theorem proving intuitionism intuitionistic logic intuitionistic type theory jean-yves girard kanada linear logic linguistics list of basic topics in logic list of fallacies list of logicians list of mathematical logic topics list of paradoxes list of rules of inference list of set theory topics logic logic in china logic in islamic philosophy logic in computer science logical atomism logical connective logical consequence logicism lotfi asker zadeh mathematical logic mathematical object mathematical proof metalogic method of analytic tableaux modal logic model theory monadic predicate calculus montague grammar mozi nagarjuna natural deduction nominalism non-monotonic logic ordinal analysis organon paraconsistent logic paradox peer review philosophical logic philosophical realism philosophy of logic platonic realism predicate logic proof-theoretic semantics proof net proposition propositional calculus provability logic quantification reason reasoning recursion theory relevance logic richard dedekind rudolf carnap rule of inference saul kripke second-order logic self-verifying theories sequent calculus set theory shahab al-din suhrawardi solomon feferman soundness structural proof theory substructural logic syllogism table of logic symbols temporal logic term logic theorem thoralf skolem truth table type theory typed lambda calculus validity well-formed formula willard van orman quine