# What does it mean "to provide semantics" in the context of formal logic?

When reading some SEP articles, this is a phrase I commonly came across, "this provides a semantics for this logic". But what does it mean?

• Maybe a ref to the relevant SEP article may help... Jun 15, 2023 at 8:11
• Having said that, see simple example regarding Propositional Logic: for classical logic the usual truth table interpretation of the propositional connectives. Jun 15, 2023 at 8:12
• Unfortunately I didn't take note of where I saw it, and I can only use phone for next few hours so it'll be a while till I can update . Requesting patience Jun 15, 2023 at 8:13
• See the entry on Classical Logic for details. Jun 15, 2023 at 8:14
• I would guess it means "Define a mapping from a (pure) syntax to a model" Jun 15, 2023 at 8:36

`P->Q` is a simple example where `P` and `Q` represent clauses and `->` represents some form of logical consequence so that `P->Q` can represent any number of meaningful expressions. It might mean 'If Bob goes into the house, then he will find his keys' or it might mean 'If the keys are on the table, then Bob left them there'. Without providing an explanation of `P->Q`, it simply is unknown what the various symbols refer to. This is what it means to give a logic a semantics in the simple sense.
In the more technical, broader sense, to give a logic a semantics isn't to give a specific series of meanings to the symbols, but to define the rules of the symbols in the abstract. For instance, in Hoare Logic `{P}C{Q}`, `{P}` and `{Q}` are again variables, but this time instead of providing specific natural language, one restricts or binds the variables to a specific domain of discourse where the former are preconditions of state, and the latter are postconditions of state and `C` is the command or operation performed in the system of computation which may be among a subset of operations provided by a a programming language specified in BNF. Such a logic is used in formal verification of the correctness of a computer program.