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We now turn our attention to a generalization of propositional logic, called “predi-cate,” or “first-order,” logic. Predicates are functions of zero or more variables that return Boolean values. Thus predicates can be true sometimes and false sometimes, depending on the values of their arguments.
e most recent version of this Exercises Booklet can be downloaded from. .ac.uk/index.html, the web page of. the Logic Manual. I have also uploaded some les with partial truth tables tables, proofs in Natural Deduction, past papers with solutions a. d lecture slides. Peter Fritz has supplied a full set of exercis.
If you tried to figure out what philosophical logic was by looking in the literature, you might easily become confused. John Burgesscharacterizes philosophical logic as a branch of formal logic: “Philosophical logic as understood here is the part of logic dealing with what classical logic leaves out, or allegedly gets wrong” (Burgess
3.1 Interpretation functions and modals. Models. Expressions are interpreted in models. A model M is a pair hD; Ii, where D is the domain, a (nonempty) set of individuals, and I is an interpretation function: an assignment of semantic values to every basic expression (constant) in the language.
In predicate logic predicate expressions are translated into predicate letters, such as Pò, QÔ, R€. e upper index is called the ‘arity index’. It indicates how many designators the predicate takes. In the above examples ‘is tall’ takes one ‘is bigger than’ takes two ‘opens ... with’ takes three
Full Screen Close Quit Why Predicate Logic • Propositional Logic lacks expressive power. • Good for structure of arguments. • Simple and elegant context to introduce syntax, semantics, proof meth-ods, soundness, completeness, ... • But, not suitable for richer domains we wish to work with. Examples: Numbers
learn how predicate logic works, first informally with many examples, later with more formal definitions, and eventually, with outlooks showing you how this system sits at the interface of many disciplines.
