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An Axiomatical Approach to T-Multi-indistinguishabilities

Javier Martín, Gaspar Mayor
2009 European Society for Fuzzy Logic and Technology  
This paper presents a new framework to model an assessment process for a complex and multidimensional syndrome such as depression.  ...  The fuzzy-logic approach allows for the representation of quantitative imprecision of the measurements and the semiotic approach allows for the representation of the qualitative imprecision of the concepts  ...  Using our framework, an assessment of patient, p 1 , by a clinician, r 1 , at time, t 1 , with outcomes o 1 and o 2 is represented as (p 1 , r 1 , (o 1 , 60) (o 2 , "moderate"), t 1 ).  ... 
dblp:conf/eusflat/MartinM09 fatcat:ntvykzwbavfglla7diz2dggokq

Pragmatists and Purists on CPT Invariance in Relativistic Quantum Field Theories [chapter]

Jonathan Bain
2015 Recent Developments in the Philosophy of Science: EPSA13 Helsinki  
theories, and purist approaches, which trade the ability to formulate realistic interacting theories for mathematical rigor.  ...  This essay analyzes Greenberg's claim in the context of the debate between pragmatist approaches to RQFTs, which trade mathematical rigor for the ability to derive predictions from realistic interacting  ...  However, lest one think that this is an improvement over the axiomatic understanding of CPT invariance, the rigor of this approach faces the following problems: (a) Expression (1) assumes that multi-particle  ... 
doi:10.1007/978-3-319-23015-3_17 fatcat:jsqkhkipv5hfrmvtzt4uj37uqy

Introspective forgetting

Hans van Ditmarsch, Andreas Herzig, Jérôme Lang, Pierre Marquis
2009 Synthese  
It can be compared to variable-forgetting as abstraction from information, wherein agents become unaware of certain variables: by employing elementary results for bisimulation, it follows that beliefs  ...  If for some t ∈ M , stateb ′ ∈ M ′ , t ′′ ∈ M ′′ : (t, t ′ ) ∈ R ′ and (t, t ′′ ) ∈ R ′′ , then add ((t ′ , i), (t ′′ , j)) to R M . Clearly, M |= ¬Kp ∧ ¬K¬p.  ...  Our modal logical context does not translate straightaway to belief contraction (see (Segerberg, 1999) for an elegant approach on which we also base our exposition).  ... 
doi:10.1007/s11229-009-9554-4 fatcat:atfbo23m45fw7ib44cd7myqgsq

A Complete Axiomatization of Knowledge and Cryptography

Mika Cohen, Mads Dam
2007 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)  
Answering the second challenge, we exhibit an axiomatization which is sound and complete relative to the underlying theory of cryptographic terms, and to an omega rule for quantifiers.  ...  Using this approach, we obtain logical characterizations of important concepts of knowledge in the security protocol literature, namely Dolev-Yao style message deduction and static equivalence.  ...  Motivated by this intuition, we introduce an indistinguishability ∼ between states, which is relativized to a permutation ρ on T ≡ .  ... 
doi:10.1109/lics.2007.4 dblp:conf/lics/CohenD07 fatcat:2uj52ixehfdwvls2dy6umjroei

Introspective Forgetting [chapter]

Hans van Ditmarsch, Andreas Herzig, Jérôme Lang, Pierre Marquis
2008 Lecture Notes in Computer Science  
It can be compared to variable-forgetting as abstraction from information, wherein agents become unaware of certain variables: by employing elementary results for bisimulation, it follows that beliefs  ...  If for some t ∈ M , stateb ′ ∈ M ′ , t ′′ ∈ M ′′ : (t, t ′ ) ∈ R ′ and (t, t ′′ ) ∈ R ′′ , then add ((t ′ , i), (t ′′ , j)) to R M . Clearly, M |= ¬Kp ∧ ¬K¬p.  ...  Our modal logical context does not translate straightaway to belief contraction (see (Segerberg, 1999) for an elegant approach on which we also base our exposition).  ... 
doi:10.1007/978-3-540-89378-3_2 fatcat:rgtewbi6ffe6dn5e3qjqervaui

A normal simulation of coalition logic and an epistemic extension

Jan Broersen, Andreas Herzig, Nicolas Troquard
2007 Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge - TARK '07  
In this paper we show how coalition logic can be reduced to the fusion of a normal modal STIT logic for agency and a standard normal temporal logic for discrete time, and how this multi-modal system can  ...  be suitably extended with an epistemic modality.  ...  Acknowledgement We would like to thank Philippe Balbiani, Olivier Gasquet and François Schwarzentruber for useful discussions concerning parts of the paper.  ... 
doi:10.1145/1324249.1324264 dblp:conf/tark/BroersenHT07 fatcat:6zvg6myqvzeobpwsweije3jjya

Indistinguishability Operators via Yager t-norms and Their Applications to Swarm Multi-Agent Task Allocation

Maria-del-Mar Bibiloni-Femenias, José Guerrero, Juan-José Miñana, Oscar Valero
2021 Mathematics  
This new type of response functions drops to zero when an agent, due to its limitations, is not able to execute a task and, therefore, is able to model a generic multi-agent system with restrictions.  ...  In order to avoid this handicap, we introduce a new kind of response functions, YPRFs, which are modelled by means of indistinguishability operators obtained via Yager t-norms.  ...  It must be stressed that the operator given by (4) is an indistinguishability operator when the t-norm T under consideration is the Dombi T 1 n Dom .  ... 
doi:10.3390/math9020190 fatcat:otugoyiognfh3pdh4hqs7cealu

Formalizing Concurrent Common Knowledge as Product of Modal Logics

Vania Costa, Mario Benevides
2005 Logic Journal of the IGPL  
As a proper semantics to concurrent common knowledge we present the closed sub-product of modal logics. We axiomatize the presented logic issuing an idea of the soundness and completeness proofs.  ...  This paper introduces a two-dimensional modal logic to represent agents' concurrent common knowledge in distributed systems.  ...  In this model, an agent can not distinguish between two cuts if his local state is the same in both cuts. If so, the cuts are said to be indistinguishable according to the agent's point of view.  ... 
doi:10.1093/jigpal/jzi049 fatcat:gg3toc7lkzdoborqejf7cldk7i

Chapter 24 Multi-Agent Systems [chapter]

Wiebe van der Hoek, Michael Wooldridge
2008 Foundations of Artificial Intelligence  
In the first category are approaches that attempt to represent the cognitive state of rational agents, and to characterize logically how such a state leads a rational agent to act.  ...  In the second category are approaches based on representing the strategic structure of a multi-agent environment, and in particular, the powers that agents have, either individually or in coalitions.  ...  In [111] , an axiomatic approach to the verification of multi-agent systems was proposed.  ... 
doi:10.1016/s1574-6526(07)03024-6 fatcat:5rmnpn6ifrdutca5uesg2vi73q

Non-extensive Hamiltonian systems follow Boltzmann's principle not Tsallis statistics—phase transitions, Second Law of Thermodynamics

D.H.E. Gross
2002 Physica A: Statistical Mechanics and its Applications  
Thus Boltzmann's principle and not Tsallis statistics describes the equilibrium properties as well the approach to equilibrium of extensive and non-extensive Hamiltonian systems.  ...  The topology of the curvature matrix C(E,N) (Hessian) of S(E,N) determines regions of pure phases, regions of phase separation, and (multi-)critical points and lines.  ...  in phase space, approach to equilibrium, Second Law Fig. 1 . 1 The compact set M(t 0 ), left side, develops into an increasingly folded "spaghetti"-like distribution M(t, t 0 ) in the phase-space with  ... 
doi:10.1016/s0378-4371(01)00646-x fatcat:ixfvagydmjf7jhukq2ygyl5nqa

Becoming Aware of Propositional Variables [chapter]

Hans van Ditmarsch, Tim French
2011 Lecture Notes in Computer Science  
Change of awareness involves that an agent becomes aware of propositional variables. We show that the logic is decidable, and we present a complete axiomatization.  ...  It uses an algebraic approach.  ...  Axiomatization Here we provide an axiomatization for DLILA, show it to be sound and complete. The initial set of axioms we consider for the logic DLILA are broken up as follows.  ... 
doi:10.1007/978-3-642-18026-2_17 fatcat:ofps5iosffgbzk5v6vgxjs6ddu

Secure information flow and program logics

Lennart Beringer, Martin Hofmann
2007 Computer Security Foundations Workshop (CSFW), Proceedings of the IEEE  
Treating base-line non-interference, multi-level security and flow sensitivity for a while language, we show how typing derivations may be used to automatically generate proofs in the program logic that  ...  Andrei Sabelfeld pointed us to the paper by Hunt and Sands.  ...  We are grateful to the members of both projects for discussions on information flow and program logics, and on earlier versions. The feedback from the reviewers is also gratefully acknowledged.  ... 
doi:10.1109/csf.2007.30 dblp:conf/csfw/BeringerH07 fatcat:ig3kwrdrwzdnlkmkmvqwoki3ce

Number-free Mathematics Based on T-norm Fuzzy Logic

Libor Behounek
2009 European Society for Fuzzy Logic and Technology  
The paper presents a form of rendering classical mathematical notions by formal theories over suitable t-norm fuzzy logics in such a way that references to real numbers are eliminated from definitions  ...  and theorems, being removed to the standard semantics of fuzzy logic.  ...  We shall briefly recapitulate the original axiomatization (adapted from [11] ) as another illustration of the number-free approach.  ... 
dblp:conf/eusflat/Behounek09 fatcat:47gv6efsdvbtzngnpabdelhtgm

Quantifying Notes [chapter]

Hans van Ditmarsch
2012 Lecture Notes in Computer Science  
This is a multi-agent Kripke structure where accessibility relations are equivalences, i.e., the 'arrows' are assumed to be transitive, symmetric, and reflexive: they are mere links between indistinguishable  ...  We will get to that below. A similar path but towards an even further generalization is as follows. In our multi-agent setting, an announcement is a public event.  ... 
doi:10.1007/978-3-642-32621-9_8 fatcat:6rfgmyd74vdotcapoioi3ljx74

Not All Those Who Wander Are Lost: Dynamic Epistemic Reasoning in Navigation

Yanjing Wang, Yanjun Li
2012 Advances in Modal Logic  
We made an in-depth study on many model theoretical aspects of the proposed framework and provide a complete axiomatization.  ...  However, when moving forward they may have new observations which can help to locate themselves by reasoning.  ...  The first author would like to thank Dr. Mehrnoosh Sadrzadeh for pointing out the problem of robot navigation during her visit to Amsterdam in 2010.  ... 
dblp:conf/aiml/WangL12 fatcat:bgwnkg5swzfylbad3nse4jbfgy
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