# Proof theory Sequent calculus

### Soundly Proving B Method Formulae Using Typed Sequent Calculus

**theory**is provided with a specific type system, expressed using set constructs, resulting in a lack of separation in a B formula between typing and set ...B

**proof**system, we can translate Zenon proofs ...

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### Proof theory for indexed nested sequents

**proof**-theoretical properties of indexed nested ...indirect

**proof**[23]. However, only an internal cut-elimination

**proof**makes a

**proof**formalism a first-class citizen for structural ...

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### Infinitary proof theory : the multiplicative additive case

**sequent**

**calculus**). The

**sequent**

**calculus**for the propositional fragment of µMALL is a finitary

**sequent**

**calculus**whose rules are the same as those of µMALL ∞ , except that ...

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### A Sequent Calculus for a Modal Logic on Finite Data Trees

**proof**

**theory**perspective, two lines of inquiry seem ...our

**sequent**

**calculus**; by completeness of the

**calculus**, the (cut) rule is admissible, but this is a semantic

**proof**rather ...

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### A Sequent Calculus with Implicit Term Representation

**proof**can be subdivided into its abstract deductive structure, often called skeleton, and a way of instantiating it with formulas which renders it a valid ...For

**proof**-search, the separation of these ...

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### Non-wellfounded proof theory for (Kleene+action)(algebras+lattices)

**sequent**system, called LKA, proofs are finitely branching, but possibly infinitely deep (i.e. not wellfounded). To prevent fallacious reasoning, we give a simple validity criterion for proofs ...

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### Normalisation & Equivalence in Proof Theory & Type Theory

**sequent**

**calculus**G4ii of [Hud89, Hud92, ...higher-order

**calculus**for it —decorating proofs with

**proof**-terms, which uses constructors cor- responding to admissible rules such as ...

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### Infinets: The parallel syntax for non-wellfounded proof-theory

**proof**-

**theory**is needed in order to apply such logics to the study of programming languages with (co)inductive data types and au- tomated (co)inductive theorem ...traditional

**proof**system ...

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### A Classical Sequent Calculus with Dependent Types

**proof**terms for statements like the full axiom of ...the

**calculus**of inductive constructions for Coq [ 6 ], and Martin-Löf’s type

**theory**for Agda [ 24 ...

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### A Classical Sequent Calculus with Dependent Types

**proof**terms for statements like the full axiom of ...the

**calculus**of inductive constructions for Coq [ 6 ], and Martin-Löf’s type

**theory**for Agda [ 24 ...

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### Symmetric dialogue games in the proof theory of linear logic

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### A bisimulation between DPLL(T) and a proof-search strategy for the focused sequent calculus

**proof**of some

**sequent**∆ ` and no previous entry ∆ 0 ` exists with ∆ 0 ⊆ ∆, or whenever it concludes that some

**sequent**∆ ` is not provable and no previous entry ∆ 0 ` exists with ∆ ⊆ ∆ 0 ...a ...

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### Dependent Type Theory in Polarised Sequent Calculus (abstract)

**proof**

**theory**, it is now well-established that continuation- passing style (CPS) translations in call by name and call by value correspond to different polarisations of formulae ( Girard , 1991 ; Danos, ...

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### Automated Reasoning Techniques as Proof-search in Sequent Calculus

**sequent**

**calculus**has major defects for

**proof**-search: the freedom with which rules can be applied leads to a very broad and redundant search ...reasonable

**proof**-search procedures. ...

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### Towards a Combinatorial Proof Theory

**sequent**

**calculus**. Whereas in the

**sequent**

**calculus**we can allow or forbid the rules on the left and/or on the right of the turnstile, in deep inference we have other ...

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### Residual theory in lambda-calculus : a formal development

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### A Nelson-Oppen based Proof System using Theory Specific Proof Systems

**proof**system that is geared towards SMT solvers and follows their conceptually modular ...Our

**proof**system makes a clear distinction between propositional and

**theory**...specific

**proof**...

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### A Proof of Weak Termination of the Simply-Typed {$\lambda\sigma$}-Calculus

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### Generic Proof Tools and Finite Group Theory

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### A Fault Tolerance protocol for ASP calculus: Design and Proof

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