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)

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Aftermath of the incompletness theorem proof

This is somewhat of a minor point about the incompletness theorem, but I'm always a little unsure: So one proves that there is a formula which is unprovable in the theory of consideration. Okay, at ...
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Is formal truth in mathematical logic a generalization of everyday, intuitive truth?

I'm trying to wrap my head around the relationship between truth in formal logic, as the value a formal expression can take on, as opposed to commonplace notions of truth. Personal background: When I ...
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Why is establishing absolute consistency of ZFC impossible?

Why is establishing the absolute consistency of ZFC impossible? What are the fundamental limitations that prohibit us with coming up with a proof? EDIT: This post seems to make the most sense. In ...
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Restricted read twice BDDs and context free grammars

Several papers give poly-time algorithms for constrained paths on labelled graphs, e.g. [1] Quote: Given an alphabet Σ, a (directed) graph G whose edges are weighted and Σ-labeled, and a formal ...
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Formal System and Formal Logical System

I was reading the Wikipedia article for Mathematical_logic. When reaching Formal_logical_systems, I was curious about its definition and clicked into its own article Logical_system, which redirected ...
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Resources for learning formal math?

I'd like to learn formal math. Preferably, though not necessarily, starting with predicate logic/first order logic rather than higher order logic. I am trying to find resources (papers, books etc.) ...
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What makes a context free grammar ambiguous?

What makes a context free grammar ambiguous?
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Can a polynomial size CFG over large alphabet describe a language, where each terminal appears even number of times?

Can a CFG over large alphabet describe a language, where each terminal appears even number of times? If yes, would the Chomsky Normal Form be polynomial in |Σ| ? EDIT: What about a language where ...
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Why can't we use memoization to parse unambiguous context-free grammars in linear time?

This is a follow-up question to Why is it hard to parse unambiguous context-free grammar in linear time? I know that Parsing Expression Grammars (PEG) can be parsed in linear time using a packrat ...
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Why is it hard to parse unambiguous context-free grammar in linear time?

From this question, I gather that whether unambiguous CF grammar can be parsed in linear time is an open problem. I'd like to know what the major roadblocks to achieve this are. That is, what made the ...
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What is the minimal axiomatization of a set of structures?

I wonder what the minimal axiomatization of a set of structures mean? I came across this term from Wikipedia: For a theory $T\in A,$ let $F(T)$ be the set of all structures that satisfy the ...
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Generating all words in a language from CFG

I have a non-ambiguous context-free grammar. Is there some standard algorithm to create list of all the words in the language the CFG defines? This can be done with an abvious brute-force search by ...
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Are axioms assumed to be true in a formal system?

In a logical system, there is assignment of truth values to the sentences in the language, and axioms are assigned the true value. A logical system is a formal system. In a formal system, there is ...
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What are the differences between a collation and a rule of formation?

I'm a beginner in mathematical logic, and currently studying(myself, without any colleague, which is sad and so asking in here) basics of formal system. Before asking a question, I'll introduce my ...
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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 ...