# INSTANTIAL NEIGHBOURHOOD LOGIC

@article{Benthem2016INSTANTIALNL, title={INSTANTIAL NEIGHBOURHOOD LOGIC}, author={Johan van Benthem and Nick Bezhanishvili and Sebastian Enqvist and Junhua Yu}, journal={The Review of Symbolic Logic}, year={2016}, volume={10}, pages={116 - 144} }

Abstract This paper explores a new language of neighbourhood structures where existential information can be given about what kind of worlds occur in a neighbourhood of a current world. The resulting system of ‘instantial neighbourhood logic’ INL has a nontrivial mix of features from relational semantics and from neighbourhood semantics. We explore some basic model-theoretic behavior, including a matching notion of bisimulation, and give a complete axiom system for which we prove completeness…

## 22 Citations

### Duality for Instantial Neighbourhood Logic via Coalgebra

- PhilosophyCMCS
- 2020

Instantial Neighbourhood Logic (INL) has been introduced recently as a language for neighbourhood frames where existential information can be given about what kind of worlds occur in a neighbourhood…

### A Propositional Dynamic Logic for Instantial Neighborhood Models

- Computer ScienceLORI
- 2017

It is shown that a number of game constructors from game logic can be adapted to this setting to ensure invariance for instantial neighborhood bisimulations, which give the appropriate bisimulation concept for INL.

### Sahlqvist Correspondence Theory for Instantial Neighbourhood Logic

- Philosophy
- 2020

In the present paper, we investigate the Sahlqvist-type correspondence theory for instantial neighbourhood logic (INL), which can talk about existential information about the neighbourhoods of a…

### Bisimulation for Weakly Expressive Coalgebraic Modal Logics

- Philosophy, Computer ScienceCALCO
- 2017

This paper proposes a notion of \Lambda-bisimulation which is parametric in a collection of predicate liftings, and proves a Hennessy-Milner style theorem, which shows that (for finitary functors) \Lamba-bisimilarity exactly matches the expressiveness of the coalgebraic modal logic arising from \L Lambda.

### IPDL : a new modal logic of computation

- Computer Science
- 2017

It is shown that a number of game constructors from game logic can be adapted to this setting to ensure invariance for instantial neighborhood bisimulations, which give the appropriate bisimulation concept for INL.

### A Propositional Dynamic Logic for Instantial Neighborhood Semantics

- Computer ScienceStud Logica
- 2019

This work proposes a new perspective on logics of computation by combining instantial neighborhood logic with bisimulation safe operations adapted from PDL, and proves that the extended logic, IPDL, is a conservative extension of dual-free game logic, and its semantics generalizes the monotone neighborhood semantics of game logic.

### Lyndon interpolation theorem of instantial neighborhood logic - constructively via a sequent calculus

- MathematicsAnn. Pure Appl. Log.
- 2020

### BISIMULATIONS FOR KNOWING HOW LOGICS

- Philosophy, Computer ScienceThe Review of Symbolic Logic
- 2021

This paper makes the first study of their model theoretical properties by introducing suitable notions of bisimulation for a family of five knowing how knowing how logics based on different notions of plans.

### Socially Friendly and Group Protecting Coalition Logics

- Computer ScienceAAMAS
- 2018

Extensions of Coalition Logic which can express statements about inter-related powers of coalitions to achieve their respective goals are considered and two new extensions are introduced and studied.

### A Tableau System for Instantial Neighborhood Logic

- Computer Science, PhilosophyLFCS
- 2018

This paper offers to the INL a tableau system that supports mechanical proof/counter-model search and there is a neighborhood of the current point in which \(\alpha _0\) universally holds and none of \(\alpha_1,...,\alpha _j\) universally fails.

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