The Role of Structural Rules in Sequent Calculi

2002 ◽  
pp. 3-37
Author(s):  
Francesco Paoli
Keyword(s):  
Sequent Calculi ◽  
Structural Rules

A First Glimpse at the Whole

2011 ◽  
pp. 272-284
Author(s):  
Reinhard Bauer ◽  
Peter Baumgartner
Keyword(s):  
Software Engineering ◽  
Natural Language ◽  
Design Patterns ◽  
Pattern Language ◽  
Pattern Languages ◽  
Structural Rules ◽  
Computer Scientists ◽  
Interesting Discussion ◽  
Open Discussion

This chapter proposes an interesting discussion on how to transfer design patterns from architecture and software engineering to education. Computer scientists and pedagogues try to define patterns and pattern languages suitable for educational needs. The main goal of their work is to enhance quality and to foster best practices of teaching. Arguably, talking about a pedagogical pattern language requires definitely thinking about and describing its taxonomy, in other words, we have to think about a “grammar,” a set of logical and structural rules that govern the composition of meta-patterns, patterns and subpatterns like sentences, phrases, and words in any given natural language. Analyzing an exemplary educational scenario, this contribution will demonstrate the applicability of Alexander’s fifteen properties of living centers in education and intends to open discussion and reflection about the important role of an educational taxonomy for classifying existing pedagogical patterns.

scholarly journals Proof theory for quantified monotone modal logics

2019 ◽  
Vol 27 (4) ◽  
pp. 478-506
Author(s):  
Sara Negri ◽  
Eugenio Orlandelli
Keyword(s):  
Proof Theory ◽  
Modal Logics ◽  
Cut Elimination ◽  
Sequent Calculi ◽  
Completeness Proof ◽  
First Order ◽  
Constant Domains ◽  
Normal Modal Logics ◽  
Order Extension

Abstract This paper provides a proof-theoretic study of quantified non-normal modal logics (NNML). It introduces labelled sequent calculi based on neighbourhood semantics for the first-order extension, with both varying and constant domains, of monotone NNML, and studies the role of the Barcan formulas in these calculi. It will be shown that the calculi introduced have good structural properties: invertibility of the rules, height-preserving admissibility of weakening and contraction and syntactic cut elimination. It will also be shown that each of the calculi introduced is sound and complete with respect to the appropriate class of neighbourhood frames. In particular, the completeness proof constructs a formal derivation for derivable sequents and a countermodel for non-derivable ones, and gives a semantic proof of the admissibility of cut.

scholarly journals Dynamic sequent calculus for the logic of Epistemic Actions and Knowledge

10.29007/mwpp ◽  
2018 ◽  
Author(s):  
Giuseppe Greco ◽  
Alexander Kurz ◽  
Alessandra Palmigiano
Keyword(s):  
Sequent Calculus ◽  
Relational Semantics ◽  
Sequent Calculi ◽  
Structural Rules ◽  
Epistemic Actions ◽  
Dynamic Logics ◽  
Display Calculi

We develop a family of display-style, cut-free sequent calculi for dynamic epistemic logics on both an intuitionistic and a classical base. Like the standard display calculi, these calculi are modular: just by modifying the structural rules according to Dosen’s principle, these calculi are generalizable both to different Dynamic Logics (Epistemic, Deontic, etc.) and to different propositional bases (Linear, Relevant, etc.). Moreover, the rules they feature agree with the standard relational semantics for dynamic epistemic logics.

Towards an algorithmic construction of cut-elimination procedures

2008 ◽  
Vol 18 (1) ◽  
pp. 81-105 ◽  
Author(s):  
AGATA CIABATTONI ◽  
ALEXANDER LEITSCH
Keyword(s):  
Substructural Logics ◽  
Cut Elimination ◽  
Sequent Calculi ◽  
Structural Rules ◽  
Algorithmic Construction ◽  
Logical Rules

We investigate cut elimination in propositional substructural logics. The problem is to decide whether a given calculus admits (reductive) cut elimination. We show that for commutative single-conclusion sequent calculi containing generalised knotted structural rules and arbitrary logical rules the problem can be decided by resolution-based methods. A general cut-elimination proof for these calculi is also provided.

LINEAR TIME IN HYPERSEQUENT FRAMEWORK

2016 ◽  
Vol 22 (1) ◽  
pp. 121-144 ◽  
Author(s):  
ANDRZEJ INDRZEJCZAK
Keyword(s):  
Proof Theory ◽  
Linear Time ◽  
Expressive Power ◽  
Sequent Calculi ◽  
Temporal Logics ◽  
Structural Rules ◽  
Proof Systems ◽  
Nonclassical Logics ◽  
Time Flow ◽  
Basic Calculus

AbstractHypersequent calculus (HC), developed by A. Avron, is one of the most interesting proof systems suitable for nonclassical logics. Although HC has rather simple form, it increases significantly the expressive power of standard sequent calculi (SC). In particular, HC proved to be very useful in the field of proof theory of various nonclassical logics. It may seem surprising that it was not applied to temporal logics so far. In what follows, we discuss different approaches to formalization of logics of linear frames and provide a cut-free HC formalization ofKt4.3, the minimal temporal logic of linear frames, and some of its extensions. The novelty of our approach is that hypersequents are defined not as finite (multi)sets but as finite lists of ordinary sequents. Such a solution allows both linearity of time flow, and symmetry of past and future, to be incorporated by means of six temporal rules (three for future-necessity and three dual rules for past-necessity). Extensions of the basic calculus with simple structural rules cover logics of serial and dense frames. Completeness is proved by Schütte/Hintikka-style argument using models built from saturated hypersequents.

A Review of Ship Surveys Practices and of Marine Casualties Partly Due to Aging Effects

2008 ◽  
Author(s):  
Cesare Mario Rizzo ◽  
Angelo Lo Nigro
Keyword(s):  
Condition Assessment ◽  
Regulatory Regime ◽  
Aging Effects ◽  
Structural Rules ◽  
The Future ◽  
Structural Failures ◽  
Common Structural Rules ◽  
Marine Accidents

The first part of this paper overviews the present international regulatory regime and the future expected developments of ship surveys, from the viewpoint of methods and criteria, identifying different degradation phenomena mainly related to aging of structures and hull equipment. The current onboard practice is recalled, both of mandatory surveys (including class surveys and particularly the new requirements introduced by the IACS Common Structural Rules) and of non mandatory industry-driven inspections. Then, reviews of few databases of marine casualties, available to authors, are presented aiming at assessing the role of aging effects in the marine accidents. Even if it should be admitted that available statistical samples are not always complete and accurate, the intent is to identify trends in the pattern of structural failures and to develop recommendations for improving the inspection regimes and procedures for condition assessment analyses by which to reduce the number and severity of such occurrences.

scholarly journals Mapping the sequence specificity of heterotypic amyloid interactions enables the identification of aggregation modifiers

2021 ◽  
Author(s):  
Nikolaos N Louros ◽  
Meine Ramakers ◽  
Emiel Michiels ◽  
Katerina Konstantoulea ◽  
Chiara Morelli ◽  
...  
Keyword(s):  
Sequence Homology ◽  
Protein Sequences ◽  
Sequence Specificity ◽  
Structural Mechanism ◽  
Structural Rules ◽  
Amyloidogenic Proteins ◽  
Systematic Understanding ◽  
Fibril Morphology ◽  
Amyloid Assembly

Heterotypic amyloid interactions between related protein sequences have been observed in functional and disease amyloids. While sequence homology seems to favour heterotypic amyloid interactions, we have no systematic understanding of the structural rules determining such interactions nor whether they inhibit or facilitate amyloid assembly. Using structure-based thermodynamic calculations and extensive experimental validation, we performed a comprehensive exploration of the defining role of sequence promiscuity in amyloid interactions. Using this knowledge, we demonstrate, using tau as a model system, that predicted cross-interactions driven by sequence homology indeed can modify nucleation, fibril morphology, kinetic assembly and cellular spreading of aggregates. We also find that these heterotypic amyloid interactions can result in the mis-localisation of brain-expressed protein sequences with prevalent activities in neurodegenerative disorders. Our findings suggest a structural mechanism by which the proteomic background can modulate the aggregation propensity of amyloidogenic proteins and discuss how such sequence-specific proteostatic perturbations could contribute to the selective cellular susceptibility of amyloid disease progression.

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