唔係好明你有咩想我睇
冇睇過你本書
就咁 down落嚟望咗兩眼
第一個 chapter 係介紹緊一套 logic 嘅最基本有啲乜
基本上會有一套 language + model theory + proof theory
而 chapter 1 係講緊前兩者
一套 formal language 要定義點為之 well-formed formula (wff)
一般 first-order predicate language 會有 terms
佢會先定義點樣為之 terms
然後點樣由 terms 再加 predicate symbol, connectives, quantifiers 去構成 wff
如果 apply 落 arithmetic
language 通常都有啲 primitives
例如會有 0 呢個 constant symbol
successor symbol 之類咁
以上只係 syntax
你要講一個 wff 係唔係 true
就會涉及 model (書中就用 structure 呢個字)
所以就有 truth in a structure/model 呢個概念
而 model 就係一個 <D, I> 嘅 pair,
D 係一個 domain of objects
I 係一個 interpretation function,話俾你聽點 interpret 啲 symbols (i.e., predicate symbols, relations symbols, terms, identity, connectives, quantifiers)
咁講 Godel incompleteness theorem 嘅書
好多時都會由呢啲基本概念開始