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The sentential rules of derivation carry over unchanged into Predicate Logic
Proofs
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A few concepts are needed give a simple portrayal of the truth and falsity of predicate logic formulas.
There is the notion of an Interpretation which consists of a Universe together with an account of how the various symbols in the predicate logic formulas apply in this Universe.
There should be a Universe, which is the collection of the objects that the formulas is about. We write, for example,
Universe = {a,b,c}
6/6/09 10Software
To learn how to interpret simple predicate logic formulas as being true or false.
This helps in proving invalidity by the technique of displaying a counter-example.
Bergmann[2008] The Logic Book Section 8.1
In propositional logic, we just took it that each of the atomic sentences either is true or is false-- we did not look into the structure of the sentences.
Truth can be discussed in more detail in predicate logic.
A start can be made in predicate logic by taking apart 'atomic' propositions and by re-phrasing what they have to say in a 'entity-has-property' way.
The constant terms a,b,c...h are used to denote entities, the predicates A,B,C...Z are used to denote properties that these entities have, and these are put together by writing the predicate first followed by the term, for example Gb.
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In predicate logic, many different styles of expression in English get cast into the same 'property-is-had-by-entity' form. For example,
6/14/07 10 Software
To start learning how to symbolize sentences using predicate logic.
Bergmann[2008] The Logic Book Sections 7.1-7.3
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You may have derivations of your own that you wish to try. Just type, paste, or drag and drop, them into the panel, select your derivation, and click 'Start from selection'.
[Often copy-and-paste won't work directly from a Web Page; however, usually drag-and-drop will work!]
You will need to use the correct logical symbols. Here they are
F ∴ F & G ∼ & ∨ ⊃ ≡ ∀ ∃ ∴
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You now have to tools to appraise sentential arguments.
Let us run through how these might be used with two examples.
Consider the argument
If no human action is free, then no one is responsible for what they do.
If no one is responsible for what they do, no one should be punished.
Therefore
If no human action is free, no one should be punished.
First it should be symbolized
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Becoming familiar with common inference patterns and being able to use them via three new rules of inference and via rewrite rules. This helps with assessing ordinary everyday reasoning such as that found in the law, in newspapers, in advertisements, etc.
Bergmann[2008] The Logic Book Section 5.5
There are many valid arguments which cannot be shown to be valid using sentential logic alone. For example,
Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.