forall x, Calgary : an introduction to formal logic /
forall x : an introduction to formal logic, Calgary
by P. D. Magnus, Tim Button ; with additions by J. Robert Loftis, Robert Trueman ; remixed and revised by Aaron Thomas-Bolduc, Richard Zach.
- 1 online resource (viii, 389 pages)
This bibliographic record is available under the Creative Commons CC0 "No Rights Reserved" license. "This booklet is based on the solutions booklet forallx: Cambridge, by Tim Button University of Cambridge used under a CC BY 4.0 license, which is based in turn on forallx, by P.D. Magnus University at Albany, State University of New York used under a CC BY 4.0 license, which was remixed & expanded by Aaron Thomas-Bolduc & Richard Zach University of Calgary"--page ii.
"This is a textbook on formal logic. The book is divided into nine parts. Part I introduces the topic and notions of logic in an informal way, without introducing a formal language yet. Parts II-IV concern truth-functional languages. In it, sentences are formed from basic sentences using a number of connectives ('or', 'and', 'not', 'if . . . then') which just combine sentences into more complicated ones. We discuss logical notions such as entailment in two ways: semantically, using the method of truth tables (in Part III) and proof-theoretically, using a system of formal derivations (in Part IV). Parts V-VII deal with a more complicated language, that of first-order logic. It includes, in addition to the connectives of truth-functional logic, also names, predicates, identity, and the so-called quantifiers. These additional elements of the language make it much more expressive than the truth-functional language, and we'll spend a fair amount of time investigating just how much one can express in it. Again, logical notions for the language of first-order logic are defined semantically, using interpretations, and proof-theoretically, using a more complex version of the formal derivation system introduced in Part IV. Part VIII discusses the extension of TFL by non-truth-functional operators for possibility and necessity: modal logic. Part IX covers two advanced topics: that of conjunctive and disjunctive normal forms and the expressive adequacy of the truth-functional connectives, and the soundness of natural deduction for TFL"--BCcampus website.