## The logic book, Volume 1This outstanding book is a leading text for symbolic or formal logic courses All techniques and concepts are presented with clear, comprehensive explanations and numerous, carefully constructed examples. Its flexible organization (all chapters are complete and self-contained) allows instructors the freedom to cover the topics they want in the order they choose. The third edition incorporates many new and updated exercises and expanded discussions on evaluating arguments and symbolization in predicate logic. A free Student Solutions Manual is packaged with every copy of the textbook. Two logic programs, Bertie III and Twootie, are available as a free download from the University of Connecticut Philosophy Department's Web site. The Web address for downloading the software is http://www.ucc.uconn.edu/~wwwphil/software.html. Bertie 3 is a proof checker for the natural deduction method and Twootie is a proof checker for the truth tree method. |

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### Contents

BASIC NOTIONS OF LOGIC | 1 |

SYMBOLIZATION | 18 |

SEMANTICS | 61 |

Copyright | |

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### Common terms and phrases

abbreviates Assumption Assumption atomic components atomic sentence biconditional compatible completed open branch conclusion Conditional Proof conjunction consistent in PD construct contains decomposed Decomposition derivation rules disjunction example Existential Instantiation existentially quantified existentially quantified sentence F F F F T F finite set functionally goal sentence Hence inconsistent in SD individual constant inductive hypothesis instantiating constant interpretation least Lemma loves material conditional mathematical induction maximally consistent Metatheorem natural deduction negation occur paraphrase partial assignment positive integers predicate logic premises proof quantificationally consistent quantificationally false quantificationally true rules of SD satisfaction assignment semantics sentence is true sentence letter sentence on line sentences of SL sentential components sentential connectives sentential logic set of sentences Simp subderivation substitution instance systematic tree tree method truth truth-functional expansions truth-functionally equivalent truth-functionally false truth-functionally inconsistent truth-functionally true truth-functionally valid truth-value assignment Universal Instantiation universally quantified sentence universe of discourse