A Characterization of Medial as Rewriting Rule

Straßburger, Lutz

doi:10.1007/978-3-540-73449-9_26

Cited by 19 publications

(29 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, we will show the stronger property that any sound linear rule satisfying (**) is already derivable by medial. First, we will require a certain relation between the webs of terms, which was defined in [Str07a]. This relation allows us to relate structural properties of graphs to derivability by medial, via the characterisation result below.…”

Section: On the Canonicity Of Switch And Medialmentioning

confidence: 99%

On linear rewriting systems for Boolean logic and some applications to proof theory

Das¹,

Straßburger²

2017

Logical Methods in Computer Science

View full text Add to dashboard Cite

Abstract. Linear rules have played an increasing role in structural proof theory in recent years. It has been observed that the set of all sound linear inference rules in Boolean logic is already coNP-complete, i.e. that every Boolean tautology can be written as a (left-and right-)linear rewrite rule. In this paper we study properties of systems consisting only of linear inferences. Our main result is that the length of any 'nontrivial' derivation in such a system is bound by a polynomial. As a consequence there is no polynomial-time decidable sound and complete system of linear inferences, unless coNP = NP. We draw tools and concepts from term rewriting, Boolean function theory and graph theory in order to access some required intermediate results. At the same time we make several connections between these areas that, to our knowledge, have not yet been presented and constitute a rich theoretical framework for reasoning about linear TRSs for Boolean logic.

show abstract

Section: On the Canonicity Of Switch And Medialmentioning

confidence: 99%

On linear rewriting systems for Boolean logic and some applications to proof theory

Das¹,

Straßburger²

2017

Logical Methods in Computer Science

View full text Add to dashboard Cite

show abstract

“…The problem for switch in isolation is solved by the correctness criteria for multiplicative linear logic, see Christian Retoré's [Ret03]. Lutz Straßburger, in [Str07a], found a criterion for the system containing only medial. For the combination of switch and medial, no criterion is known.…”

Section: Discussionmentioning

confidence: 99%

Normalisation Control in Deep Inference via Atomic Flows

Guglielmi¹,

Gundersen²

2008

Logical Methods in Computer Science

View full text Add to dashboard Cite

Abstract. We introduce 'atomic flows': they are graphs obtained from derivations by tracing atom occurrences and forgetting the logical structure. We study simple manipulations of atomic flows that correspond to complex reductions on derivations. This allows us to prove, for propositional logic, a new and very general normalisation theorem, which contains cut elimination as a special case. We operate in deep inference, which is more general than other syntactic paradigms, and where normalisation is more difficult to control. We argue that atomic flows are a significant technical advance for normalisation theory, because 1) the technique they support is largely independent of syntax; 2) indeed, it is largely independent of logical inference rules; 3) they constitute a powerful geometric formalism, which is more intuitive than syntax.

show abstract

“…It is easy to see that Problem 6.9 can be reduced to Problem 6.4 of [Str07a] which concerns only the switch and medial rules. This simplification is possible because of the decomposition theorems in [Brü03b].…”

Section: ⊓ ⊔mentioning

confidence: 99%

“…One possible way to tackle the problem is to study combinatorial properties of derivations consisting of the rules s and m, as it has been done in [Str07a].…”

Section: ⊓ ⊔mentioning

confidence: 99%

From Deep Inference to Proof Nets via Cut Elimination

Straßburger

2009

Journal of Logic and Computation

View full text Add to dashboard Cite

This paper shows how derivations in the deep inference system SKS for classical propositional logic can be translated into proof nets. Since an SKS derivation contains more information about a proof than the corresponding proof net, we observe a loss of information which can be understood as "eliminating bureaucracy". Technically this is achieved by cut reduction on proof nets. As an intermediate step between the two extremes, SKS derivations and proof nets, we will see proof graphs representing derivations in "Formalism A".

show abstract

A Characterization of Medial as Rewriting Rule

Cited by 19 publications

References 49 publications

On linear rewriting systems for Boolean logic and some applications to proof theory

On linear rewriting systems for Boolean logic and some applications to proof theory

Normalisation Control in Deep Inference via Atomic Flows

From Deep Inference to Proof Nets via Cut Elimination

Contact Info

Product

Resources

About