A Labelled Sequent Calculus for Intuitionistic Public Announcement Logic

2015 ◽  
pp. 187-202 ◽  
Author(s):  
Shoshin Nomura ◽  
Katsuhiko Sano ◽  
Satoshi Tojo
Keyword(s):  
Sequent Calculus ◽  
Public Announcement ◽  
Public Announcement Logic ◽  
Labelled Sequent Calculus

A cut-free labelled sequent calculus for dynamic epistemic logic

2020 ◽  
Vol 30 (1) ◽  
pp. 321-348
Author(s):  
Shoshin Nomura ◽  
Hiroakira Ono ◽  
Katsuhiko Sano
Keyword(s):  
Modal Logic ◽  
Epistemic Logic ◽  
Sequent Calculus ◽  
Dynamic Epistemic Logic ◽  
Kripke Semantics ◽  
Cut Rule ◽  
Public Announcement ◽  
Public Announcement Logic ◽  
Soundness And Completeness ◽  
Labelled Sequent Calculus

Abstract Dynamic epistemic logic is a logic that is aimed at formally expressing how a person’s knowledge changes. We provide a cut-free labelled sequent calculus ($\textbf{GDEL}$) on the background of existing studies of Hilbert-style axiomatization $\textbf{HDEL}$ of dynamic epistemic logic and labelled calculi for public announcement logic. We first show that the $cut$ rule is admissible in $\textbf{GDEL}$ and show that $\textbf{GDEL}$ is sound and complete for Kripke semantics. Moreover, we show that the basis of $\textbf{GDEL}$ is extended from modal logic K to other familiar modal logics including S5 with keeping the admissibility of cut, soundness and completeness.

Tableaux for Public Announcement Logic

2008 ◽  
Vol 20 (1) ◽  
pp. 55-76 ◽  
Author(s):  
P. Balbiani ◽  
H. van Ditmarsch ◽  
A. Herzig ◽  
T. de Lima
Keyword(s):  
Public Announcement ◽  
Public Announcement Logic

On axiomatizations of public announcement logic

Synthese ◽  
2013 ◽  
Vol 190 (S1) ◽  
pp. 103-134 ◽  
Author(s):  
Yanjing Wang ◽  
Qinxiang Cao
Keyword(s):  
Public Announcement ◽  
Public Announcement Logic

scholarly journals Linear Temporal Public Announcement Logic: a new perspective for reasoning the knowledge of multi-classifiers

2020 ◽  
Author(s):  
Amirhoshang Hoseinpour Dehkordi ◽  
Majid Alizadeh ◽  
Ali Movaghar
Keyword(s):  
Temporal Logic ◽  
Intelligent Systems ◽  
Time Series Data ◽  
Detection System ◽  
Transition System ◽  
Series Data ◽  
Performance Improvements ◽  
Public Announcement ◽  
Public Announcement Logic ◽  
New Perspective

Current applied intelligent systems have crucial shortcomings either in reasoning the gathered knowledge, or representation of comprehensive integrated information. To address these limitations, we develop a formal transition system which is applied to the common artificial intelligence (AI) systems, to reason about the findings. The developed model was created by combining the Public Announcement Logic (PAL) and the Linear Temporal Logic (LTL), which will be done to analyze both single-framed data and the following time-series data. To do this, first, the achieved knowledge by an AI-based system (i.e., classifiers) for an individual time-framed data, will be taken, and then, it would be modeled by a PAL. This leads to developing a unified representation of knowledge, and the smoothness in the integration of the gathered and external experiences. Therefore, the model could receive the classifier's predefined -or any external- knowledge, to assemble them in a unified manner. Alongside the PAL, all the timed knowledge changes will be modeled, using a temporal logic transition system. Later, following by the translation of natural language questions into the temporal formulas, the satisfaction leads the model to answer that question. This interpretation integrates the information of the recognized input data, rules, and knowledge. Finally, we suggest a mechanism to reduce the investigated paths for the performance improvements, which results in a partial correction for an object-detection system.

A multi-labelled sequent calculus for Topo-Logic

2020 ◽  
Vol 30 (2) ◽  
pp. 663-696
Author(s):  
Ian Shillito
Keyword(s):  
Structural Properties ◽  
Epistemic Logic ◽  
Search Strategy ◽  
Sequent Calculus ◽  
Search Tree ◽  
Topological Spaces ◽  
Label Technique ◽  
Proof Search ◽  
Labelled Sequent Calculus

Abstract We present a labelled sequent calculus for a trimodal epistemic logic exhibitied in Baltag et al. (2017, Logic, Rationality, and Interaction, pp. 330–346), an extension of the so called ‘Topo-Logic’. To the best of our knowledge, our calculus is the first proof-calculus for this logic. This calculus is obtained via an adaptation of the label technique by internalizing a semantics over topological spaces. This internalization leads to the generation of two kinds of labels in our calculus and the labelling of formulae by pairs of labels. These novelties give tools to provide a simple calculus that is intuitively connected to the semantics. We prove that this calculus enjoys many structural properties such as admissibility of cut, admissibility of contraction and invertibility of its rules. Finally, we exhibit a proof search strategy for our calculus that allows us to prove completeness in a direct way by the extraction of a countermodel from a failure of proof. To define this strategy, we design a tool for controlling the generation of labels in the construction of a search tree, although the termination of this strategy is still open.

Omega-inconsistency without cuts and nonstandard models

2016 ◽  
Vol 13 (5) ◽  
Author(s):  
Andreas Fjellstad
Keyword(s):  
Deontic Logic ◽  
Sequent Calculus ◽  
Standard Deontic Logic ◽  
Nonstandard Models ◽  
Deontic Modality ◽  
The Relationship ◽  
Labelled Sequent Calculus ◽  
Models Of Arithmetic

This paper concerns the relationship between transitivity of entailment, omega-inconsistency and nonstandard models of arithmetic. First, it provides a cut-free sequent calculus for non-transitive logic of truth STT based on Robinson Arithmetic and shows that this logic is omega-inconsistent. It then identifies the conditions in McGee (1985) for an omega-inconsistent logic as quantified standard deontic logic, presents a cut-free labelled sequent calculus for quantified standard deontic logic based on Robinson Arithmetic where the deontic modality is treated as a predicate, proves omega-inconsistency and shows thus, pace Cobreros et al.(2013), that the result in McGee (1985) does not rely on transitivity. Finally, it also explains why the omega-inconsistent logics of truth in question do not require nonstandard models of arithmetic.

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