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From: Aatu Koskensilta on 29 Jun 2010 09:38
Christopher Menzel <cmenzel(a)philebus.tamu.edu> writes:

> There is a well known collection of essays entitled _Model Theoretic
> Logics_, edited by Barwise and Feferman, that explores this notion of
> a logic in great technical detail.

Quite a nice collection it is. Of course, as you indicate, there are
logics that don't really make much sense independent of deductive
considerations. While we may provide all sorts of interesting algebraic,
topological, what not, semantics for e.g. linear logic and other
substructural logics, they aren't really defined or understood in terms
of the expressive apparatus, as is the case with first-order logic,
second-order logic, logics with generalized quantifiers, what have you.

--
Aatu Koskensilta (aatu.koskensilta(a)uta.fi)

"Wovon man nicht sprechan kann, dar�ber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 29 Jun 2010 09:39
George Greene <greeneg(a)email.unc.edu> writes:

> ANY notion of logical consequence IS a rule of inference.

No it's not.

--
Aatu Koskensilta (aatu.koskensilta(a)uta.fi)

"Wovon man nicht sprechan kann, dar�ber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Herman Jurjus on 29 Jun 2010 09:57
On 6/29/2010 3:38 PM, Aatu Koskensilta wrote:
> Christopher Menzel<cmenzel(a)philebus.tamu.edu> writes:
>
>> There is a well known collection of essays entitled _Model Theoretic
>> Logics_, edited by Barwise and Feferman, that explores this notion of
>> a logic in great technical detail.
>
> Quite a nice collection it is. Of course, as you indicate, there are
> logics that don't really make much sense independent of deductive
> considerations. While we may provide all sorts of interesting algebraic,
> topological, what not, semantics for e.g. linear logic and other
> substructural logics, they aren't really defined or understood in terms
> of the expressive apparatus, as is the case with first-order logic,
> second-order logic, logics with generalized quantifiers, what have you.

Can you say more about this? What do you mean 'understood in terms of
the expressive apparatus'?

--
Cheers,
Herman Jurjus

From: Aatu Koskensilta on 29 Jun 2010 09:58
Herman Jurjus <hjmotz(a)hetnet.nl> writes:

> Can you say more about this? What do you mean 'understood in terms of
> the expressive apparatus'?

To explain what, say, a second-order language is we explain we allow
quantifiers to bind sets, relations, properties. No such explanation is
forthcoming in case of e.g. linear logic.

--
Aatu Koskensilta (aatu.koskensilta(a)uta.fi)

"Wovon man nicht sprechan kann, dar�ber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Herman Jurjus on 29 Jun 2010 10:13
On 6/29/2010 3:58 PM, Aatu Koskensilta wrote:
> Herman Jurjus<hjmotz(a)hetnet.nl> writes:
>
>> Can you say more about this? What do you mean 'understood in terms of
>> the expressive apparatus'?
>
> To explain what, say, a second-order language is we explain we allow
> quantifiers to bind sets, relations, properties. No such explanation is
> forthcoming in case of e.g. linear logic.

How about game/dialog semantics?
Or rather, my question is: what is that crucial difference that you seem
to see between the two? Do you think dialog-semantics is less clear or
less natural as a characterization of the meaning of sentences?
If yes: why?

--
Cheers,
Herman Jurjus
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