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I'm not sure where this thread would go, but here it is...

I am reading about the property of satisfiability. And trying to get some things straight.

I saw different kinds of logics (porpositional, relational) being tested for satisfiability. I've read about models and formal systems. The book does define the formal system and says that each system has models that underlie it. But the notion of satisfiability (or consistency) is applied to a formal system.

So then propositional logic, predicate logic, etc. are SYSTEMS and then what is a model? like modus tollens and the like? I looked up wikipedia, but not sure it is the same thing. The thing is that it all is not discussed in one section, but i gathered all this information from different parts of the book.

Here's text from my book:

ps: if i expressed something unclearly or you need more details to know what I mean, please ask, i really don't know if I provided enough to understand my question.

Thanks!

I am reading about the property of satisfiability. And trying to get some things straight.

I saw different kinds of logics (porpositional, relational) being tested for satisfiability. I've read about models and formal systems. The book does define the formal system and says that each system has models that underlie it. But the notion of satisfiability (or consistency) is applied to a formal system.

So then propositional logic, predicate logic, etc. are SYSTEMS and then what is a model? like modus tollens and the like? I looked up wikipedia, but not sure it is the same thing. The thing is that it all is not discussed in one section, but i gathered all this information from different parts of the book.

Here's text from my book:

That's where I am confused.Partee_"Mathematical methods in linguistics" said:we now no longer ask whether certain axioms are true in any absolute sense, but what if anything, they might be true of. That question is equivalent to asking what models, if any, the set of axioms has.

ps: if i expressed something unclearly or you need more details to know what I mean, please ask, i really don't know if I provided enough to understand my question.

Thanks!

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