Syntax and Consequence Relations -- A Categorical Perspective (original) (raw)
On the proof-theoretic side, logic, roughly speaking, is mainly about the grammar of the language (syntax), and reasoning on this language (consequence relations). On the model-theoretic side, we further provides mathematical structures that evaluates the language (semantic models). Among these, syntax is perhaps the easiest part. What one usually does to specify the syntax is to first fix a set of variablesX , which almost always is chosen to be a countably infinite set, and then define the set of well-formed formulas Fml with variables being in X . Here in this paper we will confine ourselves to only consider language of algebraic nature. is means that our signature for the language would be algebraic, and the only formula-forming rules would be application of function symbols. Syntax in richer context with variable bindings could become much less trivial. e more interesting part of logic in our seing is how to reason with the given language, and how we provide the semantics. F...
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