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2 votes

What is meant by the expression ∃xHx, if H stands here for “is a human being”?

As always when considering quantified expressions in logic, the domain of discourse is essential. If the domain is ‘everything’, then ∃xHx is true, but if the domain is the Natural Numbers, then it is ...
PW_246's user avatar
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1 vote

What is meant by the expression ∃xHx, if H stands here for “is a human being”?

For others, this is a question of existential quantification. But you know that. Then I'll do my best to interpret your question. To review: "∃xHx" is a fragment of an artifical language. It ...
J D's user avatar
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1 vote

Computable syntax

To me it sounds like you are asking some ill-formed questions that could be clarified if you were familiar with some basic concepts. You say the following: how do I make sure my theory is "...
BurnsBA's user avatar
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1 vote

Computable syntax

You ask: So what makes one system of syntax capable of being reasonably (usefully) computable? I'm not sure that I can find a source for what makes a good formal system, however, here are some ...
J D's user avatar
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3 votes
Accepted

Computable syntax

You seem to refer to Formal Systems. A formal system is essentially a set of concepts (precise definition of objects) and axioms (atomic principles, which in the context of the current system cannot ...
RodolfoAP's user avatar
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2 votes

Computable syntax

Define your new symbols in terms of your old symbols. Pay attention to grammatical class; your new symbols should have the same class as the productions which they represent. Then, you only have to ...
Corbin's user avatar
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1 vote

Computable syntax

You can start by considering examples of reasoning within the reasoning domain you're targeting. Examples of the form, "from X and Y, Z would follow." Generate a lot of these examples. Be ...
causative's user avatar
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1 vote

Computable syntax

So what makes one system of syntax capable of being reasonably (usefully) computable? Any logical language whose logic you understand and whose vocabulary means real things. So you need to understand ...
Speakpigeon's user avatar
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0 votes

What is meant by the expression ∃xHx, if H stands here for “is a human being”?

Dijkstra and Scholten have written a book on predicate calculus that redoes traditional logic using '≡'. Traditional logic more often uses ⇔ instead of ≡; but traditional logic at the proof level ...
Rushi's user avatar
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1 vote

A question on contrapositives and predicates

In an introductory class in logic, you will learn about a thing called the material conditional, or material implication. The material conditional → is a particular kind of conditional that is a truth ...
Bumble's user avatar
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