Language, proof, and logic, Volume 1
CSLI Publications, 1999 - Philosophy - 587 pages
This textbook/software package covers first-order language in a method appropriate for first and second courses in logic. The unique on-line grading services instantly grades solutions to hundred of computer exercises. It is specially devised to be used by philosophy instructors in a way that is useful to undergraduates of philosophy, computer science, mathematics, and linguistics. The book is a completely rewritten and much improved version of The Language of First-order Logic. Introductory material is presented in a more systematic and accessible fashion. Advanced chapters include proofs of soundness and completeness for propositional and predicate logic, as well as an accessible sketch of Godel's first incompleteness theorem. The book is appropriate for a wide range of courses, from first logic courses for undergraduates (philosophy, mathematics, and computer science) to a first graduate logic course. The package includes four pieces of software: Tarski's World 5.0, a new version of the popular program that teaches the basic first-order language and its semantics; Fitch, a natural deduction proof environment for giving and checking first-order proofs; Boole, a program that facilitates the construction and checking of truth tables and related notions (tautology, tautological consequence, etc.); Submit, a program that allows students to submit exercises done with the above programs to the Grade Grinder, the automatic grading service. Grade reports are returned to the student and, if requested, to the student's instructor, eliminating the need for tedious checking of homework. All programs will be available on both Windows and Macintosh OS. Instructors do not need to use the programs themselves in order to be able to take advantage of their pedagogical value. The price of a new text/software package includes one Registration ID, which must be used each time work is submitted to the grading service. Once activated, the Registration ID is not transferable.
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The Logic of Atomic Sentences
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ambig-wffs assumption atomic sentences Axiom of Comprehension Axiom of Regularity axioms biconditional binary blocks language claim Claire clauses column conclusion conditional proof conjunction construct contains contradiction counterexample cube Cube(x disjunction Dodec(x dodecahedron domain of discourse Elim elimination English sentences example Exercises existential express F F F F T F false first-order consequence first-order language first-order logic first-order structure first-order validity Fitch formal proof free variables function symbols infer informal proof Intro introduced Large(x LeftOf Lemma logical consequence logical truth logically equivalent means methods of proof natural numbers negation negation normal form normal form notation notion noun phrases objects P A Q predicates premises Proposition prove rules satisfies sentence file sentence is true set theory simple Small(x Soundness Theorem step Submit subproof Suppose Tarski's World tautological consequence Tet(a tetrahedron things translations truth table truth values truth-functional truth-functional connectives tt-satisfiable Vx Cube(x Vx P(x