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Questions tagged [formal-systems]

A formal system is broadly defined as any well-defined system of abstract thought based on the model of mathematics. (Def: http://en.m.wikipedia.org/wiki/Formal_system)

A formal system is broadly defined as any well-defined system of abstract thought based on the model of mathematics. Reference: Wikipedia.

The entailment of the system by its logical foundation is what distinguishes a formal system from others which may have some basis in an abstract model. Often the formal system will be the basis for or even identified with a larger theory or field (e.g. Euclidean geometry) consistent with the usage in modern mathematics such as model theory.

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Understanding definition of conservative extension of a theory

From Wikipedia In mathematical logic, a logical theory $T_2$ is a (proof theoretic) conservative extension of a theory $T_1$ if the language of $T_2$ extends the language of $T_1$; every theorem of $T_1$ is a theorem of $T_2$; and any theorem…
Tim
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Can I effeciently check whether the inverse of a semantic function exists?

I'm relatively new to the fields of formal semantics/systems/languages or even model theory and therefore I miss some knowledge and experience. I try to boil the question down to the core essence of my problem. I've created a language $\mathcal{L}$…
Alex
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Does a formal system having inference rules imply that it is a logic system?

From Wikipedia Formal systems in mathematics consist of the following elements: A finite set of symbols (i.e. the alphabet), that can be used for constructing formulas (i.e. finite strings of symbols). A grammar, which tells how well-formed…
Tim
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theory, theorems and axioms

According to Wikipedia In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. Usually a deductive system is understood from context. An element $\phi\in T$ of a theory $T$ is then called an…
Tim
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Are theorems (not axioms) listed as a part of a formal system?

Are theorems derived from a formal system a part of that formal system? In other words, do we view a formal system as a shorter way of listing all the theorems that flow from such a system? In other words, can a formal system be viewed as a recipe…
TKN
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Could formal systems be viewed as a short version of saying what I believe in without necessary listing all theorems which flow from that system?

Lets say that I tell to a person "A" that I believe that the Got exists. For the person "A" it seems therefore obvious to imagine that I also believe in a lot of things that flow from such a statement. But lets say, that me and the person "A" made a…
TKN
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How do I find out effectively what particular formal system I'm using in any particular moment when doing math in school?

I would like to know: How to find out in what particular formal system I am working (what axioms, rules of inference and formal language am I assuming) when they don't specify me in a school? For example, in what particular formal system in…
TKN
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What are "non-trivial formal systems"?

In Godel’s incompleteness theorem, his two statements relate to “non-trivial formal system”, but how are these determined? Is 1+1=2 one of these? What about P vs NP?
Goodwin Lu
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Is there a formal system which is generally accepted, and how is it called?

I read the question at Gödel's Incompleteness Theorem -- meta-reasoning "loophole"? about Gödel's incompleteness theorem. My question is little about the contents of that other question. Rather, it is about terminology. How is the thinking system or…
Daniel S.
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Are interpretation and formalization inverse to each other?

I am not sure if I understand this correctly. Please correct me. In a formal system, an interpretation is a mapping from its formal language to one of its structures ie models. an formalization is a mapping from one of its models to its formal …
Tim
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