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Soundness of Propositional Logics through Morphisms

Model-theory and Proof-theory in Propositional LogicWhat's the difference between a logic, an internal logic (language) of a category, an internal logic of a topos and a type theory?Models and signatures for propositional logicIs negation introduction derivable in the natural deduction system of intuitionistic propositional logic?Understanding an interpretation of Godel's first incompleteness theorem.Cut Law For AbjunctionTruth tables in propositional calculus: semantic or syntactic in nature?$mathbb Q$ topological semantics for intuitionistic propositional logicDisproving: If $(Gammavdash(phi,lorpsi))$, either $(Gammavdashphi)$ or $(Gammavdashpsi)$ is trueAxiomatic proof of $vdash p rightarrow ((prightarrow q) rightarrow q)$

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I'm trying to prove that propositional logic is sound and complete, using the notion of morphism between consequence systems, i.e., pairs $langle C,vdashrangle$ where C is a signature and $vdash:wp L(C)rightarrow wp L(C)$ is a map between the language generated by the signature.

More specifically, I'm trying to find a morphism

$h:langle C,vdashranglerightarrowlangle C,vDashrangle$

which by definition would imply that

$h(Gamma^vdash)subseteq(h(Gamma))^vDash$

Is this possible? And if so, what morphism could I use?

logic

share|cite|improve this question

asked Mar 21 at 23:53

Tiago CostaTiago Costa

12

$endgroup$

add a comment | 

0

$begingroup$

I'm trying to prove that propositional logic is sound and complete, using the notion of morphism between consequence systems, i.e., pairs $langle C,vdashrangle$ where C is a signature and $vdash:wp L(C)rightarrow wp L(C)$ is a map between the language generated by the signature.

More specifically, I'm trying to find a morphism

$h:langle C,vdashranglerightarrowlangle C,vDashrangle$

which by definition would imply that

$h(Gamma^vdash)subseteq(h(Gamma))^vDash$

Is this possible? And if so, what morphism could I use?

logic

share|cite|improve this question

asked Mar 21 at 23:53

Tiago CostaTiago Costa

12

$endgroup$

add a comment | 

$begingroup$

I'm trying to prove that propositional logic is sound and complete, using the notion of morphism between consequence systems, i.e., pairs $langle C,vdashrangle$ where C is a signature and $vdash:wp L(C)rightarrow wp L(C)$ is a map between the language generated by the signature.

More specifically, I'm trying to find a morphism

$h:langle C,vdashranglerightarrowlangle C,vDashrangle$

which by definition would imply that

$h(Gamma^vdash)subseteq(h(Gamma))^vDash$

Is this possible? And if so, what morphism could I use?

logic

share|cite|improve this question

asked Mar 21 at 23:53

Tiago CostaTiago Costa

12

$endgroup$

share|cite|improve this question

asked Mar 21 at 23:53

Tiago CostaTiago Costa

12

share|cite|improve this question

asked Mar 21 at 23:53

Tiago CostaTiago Costa

12

asked Mar 21 at 23:53

Tiago CostaTiago Costa

12

asked Mar 21 at 23:53

Tiago CostaTiago Costa

12