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Two most important fields that logic plays vital role are:

1. Formal Language specification and verification.
2. Fixed parameter tractable classes.

Seems needs some clarification, in formal languages you need to extremely work on logic, for clarification take a look at:

1. Formal language.
2. Introduction to $Z$.

In short: 1. Definition of language needs logic, 2: Justice of it's procedures needs logic, 3. verification procedures need logic.

I should mention that this is different from compiler design or ..., This is "Formal" definition of languages, main reason to do this is proving correctness of language or model, also having a formal proof. This can be used in verification of software models, finding errors before implementing, finding deadlocks again before implementing, ...., For software which simulate this you can take a look at NModel.

Now why in Fixed parameter tractable problems you need to work with logic, You can divide classes of Fixed parameter tractability with different levels of logic, this are can be converted to each other : logic to automata, automata to graph, and vice verse, But if you be an expert in logic you can divide and decide on them simply, most important theorem (after Robertson and Seymour theorem), in this field is Courcelle's theorem. for more information read Meta Algorithmic Theorem survey.

Two most important fields that logic plays vital role are:

1. Formal Language specification and verification.
2. Fixed parameter tractable classes.

Seems needs some clarification, in formal languages you need to extremely work on logic, for clarification take a look at:

1. Formal language.
2. Introduction to $Z$.

In short: 1. Definition of language needs logic, 2: Justice of it's procedures needs logic, 3. verification procedures need logic.

I should mention that this is different from compiler design or ..., This is "Formal" definition of languages, main reason to do this is proving correctness of language or model, also having a formal proof. This can be used in verification of software models, finding errors before implementing, finding deadlocks again before implementing, ...., For software which simulate this you can take a look at NModel.

Now why in Fixed parameter tractable problems you need to work with logic, You can divide classes of Fixed parameter tractability with different levels of logic, they can be converted to each other : logic to automata, automata to graph, and vice verse, But if you be an expert in logic you can divide and decide on them simply, most important theorem (after Robertson and Seymour theorem), in this field is Courcelle's theorem. for more information read Meta Algorithmic Theorem survey.

Two most important fields that logic plays vital role are:

1. Formal Language specification and verification.
2. Fixed parameter tractable classes.

I can't define them in two paragraph, but simple survey will introduce you to them.

Seems needs some clarification, in formal languages you need to extremely work on logic, for clarification take a look at:

1. Formal language.
2. Introduction to $Z$.

In short: 1. Definition of language needs logic, 2: Justice of it's procedures needs logic, 3. verification procedures need logic.

I should mention that this is different from compiler design or ..., This is "Formal" definition of languages, main reason to do this is proving correctness of language or model, also having a formal proof. This can be used in verification of software models, finding errors before implementing, finding deadlocks again before implementing, ....

Now why in Fixed parameter tractable problems you need to work with logic, You can divide classes of Fixed parameter tractability with different levels of logic, this are can be converted to each other : logic to automata, automata to graph, and vice verse, But if you be an expert in logic you can divide and decide on them simply, most important theorem (after Robertson and Seymour theorem), in this field is Courcelle's theorem. for more information read Meta Algorithmic Theorem survey.

P.S: the new update is response to Raphael's comment, I don't think this information is useful for the OP but just for clarification I add them.

Two most important fields that logic plays vital role are:

1. Formal Language specification and verification.
2. Fixed parameter tractable classes.

Seems needs some clarification, in formal languages you need to extremely work on logic, for clarification take a look at:

1. Formal language.
2. Introduction to $Z$.

In short: 1. Definition of language needs logic, 2: Justice of it's procedures needs logic, 3. verification procedures need logic.

I should mention that this is different from compiler design or ..., This is "Formal" definition of languages, main reason to do this is proving correctness of language or model, also having a formal proof. This can be used in verification of software models, finding errors before implementing, finding deadlocks again before implementing, ...., For software which simulate this you can take a look at NModel.

Now why in Fixed parameter tractable problems you need to work with logic, You can divide classes of Fixed parameter tractability with different levels of logic, this are can be converted to each other : logic to automata, automata to graph, and vice verse, But if you be an expert in logic you can divide and decide on them simply, most important theorem (after Robertson and Seymour theorem), in this field is Courcelle's theorem. for more information read Meta Algorithmic Theorem survey.

Two most important fields that logic plays vital role are:

1. Formal Language specification and verification.
2. Fixed parameter tractable classes.

I can't define them in two paragraph, but simple survey will introduce you to them.

Seems needs some clarification, in formal languages you need to extremely work on logic, for clarification take a look at:

1. Formal language.
2. Introduction to $Z$.

In short: 1. Definition of language logic, 2: Justice of it's procedures needs logic, 3. verification procedures need logic.

I should mention that this is different from compiler design or ..., This is "Formal" definition of languages, main reason to do this is proving correctness of language.

Now why in Fixed parameter tractable problems you need to work with logic, You can divide classes of Fixed parameter tractability with different levels of logic, this are can be converted to each other : logic to automata, automata to graph, and vice verse, But if you be an expert in logic you can divide and decide on them simply, most important theorem (after Robertson and Seymour theorem), in this field is Courcelle's theorem. for more information on Meta Algorithmic Theorem survey.

P.S: the new update is response to Raphael's comment, I don't think this information is useful for the OP but just for clarification I add them.

Two most important fields that logic plays vital role are:

1. Formal Language specification and verification.
2. Fixed parameter tractable classes.

I can't define them in two paragraph, but simple survey will introduce you to them.

Seems needs some clarification, in formal languages you need to extremely work on logic, for clarification take a look at:

1. Formal language.
2. Introduction to $Z$.

In short: 1. Definition of language needs logic, 2: Justice of it's procedures needs logic, 3. verification procedures need logic.

I should mention that this is different from compiler design or ..., This is "Formal" definition of languages, main reason to do this is proving correctness of language or model, also having a formal proof. This can be used in verification of software models, finding errors before implementing, finding deadlocks again before implementing, ....

Now why in Fixed parameter tractable problems you need to work with logic, You can divide classes of Fixed parameter tractability with different levels of logic, this are can be converted to each other : logic to automata, automata to graph, and vice verse, But if you be an expert in logic you can divide and decide on them simply, most important theorem (after Robertson and Seymour theorem), in this field is Courcelle's theorem. for more information read Meta Algorithmic Theorem survey.

P.S: the new update is response to Raphael's comment, I don't think this information is useful for the OP but just for clarification I add them.