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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.
Syntactic rules to specify the well-formed formulas of predicate logic: (8)a.If t 1;t 2;:::;t n are individual terms and P is an n-place predicate, then P(t 1;t 2;:::;t n) is a w . b.If xis an individual variable and is a w , then 9x and 8x are w s. c.If and are w s, then : , ( ^ ), ( _ ), ( ! ), and ( $ ) are w s.
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.
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.
The language of predicate logic retains all the vocabulary of propositional logic, including the connectives but adds predicates and individual constants, variables, which act as place-‐holders for individual constants, and quantifiers, which interact with variables.
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
