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13 Cards in this Set
- Front
- Back
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Semantics |
Meaning of symbols - for the purpose to codify words and concepts on language |
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Syntax |
Rules that symbols within a formal language must follow - for the purpose to show which arguments are valid |
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Validity |
the truth of the premise implies the truth of the conclusion (deductive argument) |
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Symbols |
Atomic expression of a formal language |
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Formation Rules |
rules on what strings of symbols are formulas (grammatical or well-formed) |
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Formal Systems |
Formal Language + Deductive Apparatus (this generates a special subset of the well-formed formulas that are the "theorems" of the system) |
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Theorem |
A formula producible by the deductive apparatus |
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Axioms |
Formulas that are 'starting points' or "free theorems" |
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Inference Rules |
Specifications for what transitions between formulas are allowed. (formal Systems can have only axioms, only inference Rules or a combination of both) |
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Derivation |
An explicit line by line demonstration of how to produce a theorem according to the rules and axioms of the formal system. |
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L1 BASIC SYMBOLS |
BASIC SYMBOLSSentence letters: P, . . . , Z (including numerical subscripts, e.g. P4, Q23, etc.) Connectives: ¬, → Punctuation: ),( |
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L1 FORMATION RULES: |
Any sentence letter is a sentence If φ is a sentence, then ¬φ is a sentence If φ and ψ are a sentences, then (φ → ψ) is a sentence Nothing else is a sentence of L1 unless it can b |
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L1 Terminology |
Atomic Sentance - containing no connectives at all. eg. Q Moleclular Sentance - a sentantance contraining atleast one connective. eg. (X->Y) Negation (un-negation) - [¬] a negation of a symbol or Conditional - a sentance of the form(φ → ψ) is a conditional[if ___ then ___] (if antecedent then consequent) |
