Results 1  10
of
1,568
On the Proof Complexity of Deep Inference
, 2000
"... We obtain two results about the proof complexity of deep inference: 1) deepinference proof systems are as powerful as Frege ones, even when both are extended with the Tseitin extension rule or with the substitution rule; 2) there are analytic deepinference proof systems that exhibit an exponential ..."
Abstract

Cited by 38 (14 self)
 Add to MetaCart
We obtain two results about the proof complexity of deep inference: 1) deepinference proof systems are as powerful as Frege ones, even when both are extended with the Tseitin extension rule or with the substitution rule; 2) there are analytic deepinference proof systems that exhibit
Classical categories and deep inference
"... Deep inference is a prooftheoretic notion in which proof rules apply arbitrarily deeply inside a formula. We show that the essense of deep inference is the bifunctorality of the connectives. We demonstrate that, when given an inequational theory that models cutreduction, a deep inference calculus ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Deep inference is a prooftheoretic notion in which proof rules apply arbitrarily deeply inside a formula. We show that the essense of deep inference is the bifunctorality of the connectives. We demonstrate that, when given an inequational theory that models cutreduction, a deep inference calculus
Deep Inference and the Calculus of Structures
, 2006
"... The calculus of structures is a new proof theoretical formalism, introduced by myself in 1999 and initially developed by members of my group in Dresden since 2000. It exploits a new symmetry made possible by deep inference. We can present deductive systems in the calculus of structures and analyse t ..."
Abstract
 Add to MetaCart
The calculus of structures is a new proof theoretical formalism, introduced by myself in 1999 and initially developed by members of my group in Dresden since 2000. It exploits a new symmetry made possible by deep inference. We can present deductive systems in the calculus of structures and analyse
Deep Inference for Hybrid Logic
, 2007
"... This paper describes work in progress on using deep inference for designing a deductive system for hybrid logic. We will see a cutfree system and prove its soundness and completeness. An immediate observation about the system is that there is no need for additional rewrite rules as in Blackburn’s ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
This paper describes work in progress on using deep inference for designing a deductive system for hybrid logic. We will see a cutfree system and prove its soundness and completeness. An immediate observation about the system is that there is no need for additional rewrite rules as in Blackburn’s
Implementing Deep Inference in TOM
, 2005
"... The calculus of structures is a proof theoretical formalism which generalizes sequent calculus with the feature of deep inference: in contrast to sequent calculus, the calculus of structures does not rely on the notion of main connective and, like in term rewriting, it permits the application of inf ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The calculus of structures is a proof theoretical formalism which generalizes sequent calculus with the feature of deep inference: in contrast to sequent calculus, the calculus of structures does not rely on the notion of main connective and, like in term rewriting, it permits the application
Implementing deep inference in TOM
 In Structures and Deduction (SD’05), ICALP Workshop
, 2005
"... Abstract. The calculus of structures is a proof theoretical formalism which generalizes sequent calculus with the feature of deep inference: in contrast to sequent calculus, the calculus of structures does not rely on the notion of main connective and, like in term rewriting, it permits the applicat ..."
Abstract
 Add to MetaCart
Abstract. The calculus of structures is a proof theoretical formalism which generalizes sequent calculus with the feature of deep inference: in contrast to sequent calculus, the calculus of structures does not rely on the notion of main connective and, like in term rewriting, it permits
ON ANALYTICITY IN DEEP INFERENCE
"... In this note, we discuss the notion of analytic inference rule for propositional logics in the calculus of structures (CoS) [4]. CoS generalises the sequent calculus and preserves all its prooftheoretic properties. There is no established notion of analytic rule outside of the sequent calculus, and ..."
Abstract
 Add to MetaCart
1. A CoS (inference) rule is a polynomialtime computable binary relation over the set of formulae; by writing A r −−− B we indicate that formulae A (premiss) and B (conclusion) are in the inferencerule relation r. Deepinference rules are the rules such that, for every context K { } where the hole
A PERSONAL PERSPECTIVE ON DEEP INFERENCE
"... Deep inference is a young area in proof theory, which is the discipline that studies mathematical proofs. It is a new methodology for designing proof formalisms that generalise those introduced by Gentzen, in the ’30s, for the presentation of proof systems [Gen69]. The conceptual origins of deep inf ..."
Abstract
 Add to MetaCart
Deep inference is a young area in proof theory, which is the discipline that studies mathematical proofs. It is a new methodology for designing proof formalisms that generalise those introduced by Gentzen, in the ’30s, for the presentation of proof systems [Gen69]. The conceptual origins of deep
What is a Normal Deep Inference Derivation?
"... Deep inference systems consist of two fragments... ..."
Learning Deep Inference Machines
"... Introduction. The traditional approach to structured prediction problems is to craft a graphical model structure, learn parameters for the model, and perform inference using an efficient – and usually approximate– inference approach, including, e.g., graph cut methods, belief propagation, and variat ..."
Abstract
 Add to MetaCart
Introduction. The traditional approach to structured prediction problems is to craft a graphical model structure, learn parameters for the model, and perform inference using an efficient – and usually approximate– inference approach, including, e.g., graph cut methods, belief propagation
Results 1  10
of
1,568