scholarly journals The Ceteris Paribus Structure of Logics of Game Forms

2015 ◽  
Vol 53 ◽  
pp. 91-126 ◽  
Author(s):  
Davide Grossi ◽  
Emiliano Lorini ◽  
Francois Schwarzentruber
Keyword(s):  
Modal Logic ◽  
Dynamic Logic ◽  
Strategic Interaction ◽  
Equivalence Classes ◽  
Finite Sets ◽  
Ceteris Paribus ◽  
Coalition Logic ◽  
Game Forms

The article introduces a ceteris paribus modal logic, called CP, interpreted on the equivalence classes induced by finite sets of propositional atoms. This logic is studied and then used to embed three logics of strategic interaction, namely atemporal STIT, the coalition logic of propositional control (CL−PC) and the starless fragment of the dynamic logic of propositional assignments (DL−PA). The embeddings highlight a common ceteris paribus structure underpinning the key operators of all these apparently very different logics and show, we argue, remarkable similarities behind some of the most influential formalisms for reasoning about strategic interaction

scholarly journals The Ceteris Paribus Structure of Logics of Game Forms (Extended Abstract)

2017 ◽  
Author(s):  
Davide Grossi ◽  
Emiliano Lorini ◽  
François Schwarzentruber
Keyword(s):  
Normal Form ◽  
Dynamic Logic ◽  
Satisfiability Problem ◽  
Ceteris Paribus ◽  
Coalition Logic ◽  
Polynomial Reduction ◽  
Complexity Result ◽  
Game Forms

We present a simple Ceteris Paribus Logic (CP) and study its relationship with existing logics that deal with the representation of choice and power in games in normal form including atemporal STIT, Coalition Logic of Propositional Control (CL-PC) and Dynamic Logic of Propositional Assignments (DL-PA). Thanks to the polynomial reduction of the satisfiability problem for atemporal STIT in the satisfiability problem for CP, we obtain a complexity result for the latter problem.

On monotone modalities and adjointness

2011 ◽  
Vol 21 (2) ◽  
pp. 383-416
Author(s):  
MARTA BÍLKOVÁ ◽  
JIŘÍ VELEBIL ◽  
YDE VENEMA
Keyword(s):  
Modal Logic ◽  
Finite Sets ◽  
Logical Connection

We fix a logical connection (Stone ˧ Pred : Setop → BA given by 2 as a schizophrenic object) and study coalgebraic modal logic that is induced by a functor T: Set → Set that is finitary and standard and preserves weak pullbacks and finite sets. We prove that for any such T, the cover modality nabla is a left (and its dual delta is a right) adjoint relative to ω. We then consider monotone unary modalities arising from the logical connection and show that they all are left (or right) adjoints relative to ω.

scholarly journals A Modal Logic for Joint Abilities under Strategy Commitments

2020 ◽  
Author(s):  
Zhaoshuai Liu ◽  
Liping Xiong ◽  
Yongmei Liu ◽  
Yves Lespérance ◽  
Ronghai Xu ◽  
...  
Keyword(s):  
Modal Logic ◽  
Temporal Logic ◽  
Dynamic Logic ◽  
Research Area ◽  
Multi Agent Systems ◽  
Logical Frameworks ◽  
Dominated Strategies ◽  
Multi Agent ◽  
Active Research ◽  
Active Research Area

Representation and reasoning about strategic abilities has been an active research area in AI and multi-agent systems. Many variations and extensions of alternating-time temporal logic ATL have been proposed. However, most of the logical frameworks ignore the issue of coordination within a coalition, and are unable to specify the internal structure of strategies. In this paper, we propose JAADL, a modal logic for joint abilities under strategy commitments, which is an extension of ATL. Firstly, we introduce an operator of elimination of (strictly) dominated strategies, with which we can represent joint abilities of coalitions. Secondly, our logic is based on linear dynamic logic (LDL), an extension of linear temporal logic (LTL), so that we can use regular expressions to represent commitments to structured strategies. We analyze valid formulas in JAADL, give sufficient/necessary conditions for joint abilities, and show that model checking memoryless JAADL is in EXPTIME.

scholarly journals Equivalence classes of functions on finite sets

1982 ◽  
Vol 5 (4) ◽  
pp. 745-762
Author(s):  
Chong-Yun Chao ◽  
Caroline I. Deisher
Keyword(s):  
Equivalence Class ◽  
Equivalence Classes ◽  
Permutation Groups ◽  
Weak Equivalence ◽  
Finite Sets ◽  
The Family ◽  
Polya's Theorem ◽  
Finite Set ◽  
Pólya’S Theorem

By using Pólya's theorem of enumeration and de Bruijn's generalization of Pólya's theorem, we obtain the numbers of various weak equivalence classes of functions inRDrelative to permutation groupsGandHwhereRDis the set of all functions from a finite setDto a finite setR,Gacts onDandHacts onR. We present an algorithm for obtaining the equivalence classes of functions counted in de Bruijn's theorem, i.e., to determine which functions belong to the same equivalence class. We also use our algorithm to construct the family of non-isomorphicfm-graphs relative to a given group.

scholarly journals Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences

2008 ◽  
Vol 38 (1) ◽  
pp. 83-125 ◽  
Author(s):  
Johan van Benthem ◽  
Patrick Girard ◽  
Olivier Roy
Keyword(s):  
Modal Logic ◽  
Ceteris Paribus

ON THE REGULARITY OF SETS OF MULTI-ACCEPTED STRINGS OF A NON-DETERMINISTIC FINITE AUTOMATON

2009 ◽  
Vol 02 (04) ◽  
pp. 717-726
Author(s):  
L. K. Waters ◽  
J. K. Grieshop
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Equivalence Classes ◽  
Deterministic Finite Automaton ◽  
Finite Sets ◽  
Nondeterministic Finite Automata ◽  
Labeling Approach ◽  
Acceptance Levels ◽  
Labeling Method

In this paper we establish the regularity of various sets of multi-accepted strings of nondeterministic finite automata. Regularity follows from the existence of accepting automata constructed by introducing a vector labeling method which generalizes the subset labeling approach. In each set the acceptance levels of the strings correspond to finite sets of additive equivalence classes of non-negative integers.

Modal Logics for Reasoning about Multiagent Systems

2011 ◽  
pp. 1089-1094
Author(s):  
Nikolay V. Shilov ◽  
Natalia Garanina
Keyword(s):  
Modal Logic ◽  
Multiagent Systems ◽  
Dynamic Logic ◽  
Modal Logics ◽  
Kripke Models ◽  
Linear Orders ◽  
Propositional Dynamic Logic ◽  
Combined Logics ◽  
Logic Of Knowledge ◽  
Scientific Context

It becomes evident in recent years a surge of interest to applications of modal logics for specification and validation of complex systems. It holds in particular for combined logics of knowledge, time and actions for reasoning about multiagent systems (Dixon, Nalon & Fisher, 2004; Fagin, Halpern, Moses & Vardi, 1995; Halpern & Vardi, 1986; Halpern, van der Meyden & Vardi, 2004; van der Hoek & Wooldridge, 2002; Lomuscio, & Penczek, W., 2003; van der Meyden & Shilov, 1999; Shilov, Garanina & Choe, 2006; Wooldridge, 2002). In the next paragraph we explain what are logics of knowledge, time and actions from a viewpoint of mathematicians and philosophers. It provides us a historic perspective and a scientific context for these logics. For mathematicians and philosophers logics of actions, time, and knowledge can be introduced in few sentences. A logic of actions (ex., Elementary Propositional Dynamic Logic (Harel, Kozen & Tiuryn, 2000)) is a polymodal variant of a basic modal logic K (Bull & Segerberg, 2001) to be interpreted over arbitrary Kripke models. A logic of time (ex., Linear Temporal Logic (Emerson, 1990)) is a modal logic with a number of modalities that correspond to “next time”, “always”, “sometimes”, and “until” to be interpreted in Kripke models over partial orders (discrete linear orders for LTL in particular). Finally, a logic of knowledge or epistemic logic (ex., Propositional Logic of Knowledge (Fagin, Halpern, Moses & Vardi, 1995; Rescher, 2005)) is a polymodal variant of another basic modal logic S5 (Bull & Segerberg, 2001) to be interpreted over Kripke models where all binary relations are equivalences.

Modal Logic

1980 ◽  
Author(s):  
Brian F. Chellas
Keyword(s):  
Modal Logic
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