Timo Lang
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View article: Bifurcation Logic: Separation Through Ordering
Bifurcation Logic: Separation Through Ordering Open
We introduce Bifurcation Logic, BL, which combines a basic classical modality with separating conjunction * together with its naturally associated multiplicative implication, that is defined using the modal ordering. Specifically, a formul…
View article: Analytic Proofs for Tense Logic
Analytic Proofs for Tense Logic Open
The first algorithm to transform a proof in Nishimura’s sequent calculus $$\textbf{GKt}$$ for tense logic $$\textbf{Kt}$$ into an analytic proof of the same sequent is presented. In an analytic proof, every rule instance is analytic i.…
View article: A Simple Token Game and its Logic
A Simple Token Game and its Logic Open
We introduce a simple game of resource-conscious reasoning. In this two-player game, players P and O place tokens of positive and negative polarity onto a game board according to certain rules. P wins if she manages to match every negative…
View article: Cut-Restriction: From Cuts to Analytic Cuts
Cut-Restriction: From Cuts to Analytic Cuts Open
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations into decidability, complexity…
View article: Cut-restriction: from cuts to analytic cuts
Cut-restriction: from cuts to analytic cuts Open
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability, compl…
View article: Some Analytic Systems of Rules
Some Analytic Systems of Rules Open
We define two simple systems of rules, i.e. calculi with a global condition on the order of rule instances in a proof, for the modal logics of shift-reflexive and Euclidean frames respectively. Cut-elimination, and therefore the subformula…
View article: From Truth Degree Comparison Games to Sequents-of-Relations Calculi for Gödel Logic
From Truth Degree Comparison Games to Sequents-of-Relations Calculi for Gödel Logic Open
We introduce a game for (extended) Gödel logic where the players’ interaction stepwise reduces claims about the relative order of truth degrees of complex formulas to atomic truth comparison claims. Using the concept of disjunctive game st…
View article: A theory of cut-restriction: first steps
A theory of cut-restriction: first steps Open
Cut-elimination is the bedrock of proof theory. It is the algorithm that eliminates cuts from a sequent calculus proof that leads to cut-free calculi and applications. Cut-elimination applies to many logics irrespective of their semantics.…
View article: From Semantic Games to Provability: The Case of Gödel Logic
From Semantic Games to Provability: The Case of Gödel Logic Open
We present a semantic game for Gödel logic and its extensions, where the players’ interaction stepwise reduces arbitrary claims about the relative order of truth degrees of complex formulas to atomic ones. The paper builds on a previously …
View article: Decidability and Complexity in Weakening and Contraction Hypersequent Substructural Logics
Decidability and Complexity in Weakening and Contraction Hypersequent Substructural Logics Open
We establish decidability for the infinitely many axiomatic extensions of the commutative Full Lambek logic with weakening FLew (i.e. IMALLW) that have a cut-free hypersequent proof calculus. Specifically: every analytic structural rule ex…
View article: Games, Modalities and Analytic Proofs in Nonclassical Logics
Games, Modalities and Analytic Proofs in Nonclassical Logics Open
The present thesis deals with three different topics in the proof theory of nonclassical logics. We first investigate logics which are presented as analytic hypersequent calculi. Using a projection of cutfree hypersequent proofs onto proof…
View article: BOUNDED-ANALYTIC SEQUENT CALCULI AND EMBEDDINGS FOR HYPERSEQUENT LOGICS
BOUNDED-ANALYTIC SEQUENT CALCULI AND EMBEDDINGS FOR HYPERSEQUENT LOGICS Open
A sequent calculus with the subformula property has long been recognised as a highly favourable starting point for the proof theoretic investigation of a logic. However, most logics of interest cannot be presented using a sequent calculus …
View article: Decidability and Complexity in Weakening and Contraction Hypersequent Substructural Logics
Decidability and Complexity in Weakening and Contraction Hypersequent Substructural Logics Open
We establish decidability for the infinitely many axiomatic extensions of the commutative Full Lambek logic with weakening FLew (i.e. IMALLW) that have a cut-free hypersequent proof calculus (specifically: every analytic structural rule ex…