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Axiomatizing Causal Reasoning [article]

Joseph Y. Halpern
2000 arXiv   pre-print
Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here.  ...  It is shown that to reason about causality in the most general third class, we must extend the language used by Galles and Pearl.  ...  The way we go about axiomatizing causal reasoning depends on two critical factors: • how we model causality, and • the language that we use to reason about it.  ... 
arXiv:cs/0005030v1 fatcat:gbdtcpf6fvea7j2momdlv3qd6q

Axiomatizing Causal Reasoning [article]

Joseph Y. Halpern
2014 arXiv   pre-print
Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here.  ...  It is shown that to reason about causality in the most general third class, we must extend the language used by Galles and Pearl.  ...  The way we go about axiomatizing causal reasoning depends on two critical factors: • how we model causality, and • the language that we use to reason about it.  ... 
arXiv:1408.1482v1 fatcat:hcycl4lggbhw5cfszrzb5c3vvy

Axiomatizing Causal Reasoning

J. Y. Halpern
2000 The Journal of Artificial Intelligence Research  
Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here.  ...  It is shown that to reason about causality in the most general third class, we must extend the language used by Galles and Pearl.  ...  The way we go about axiomatizing causal reasoning depends on two critical factors: • how we model causality, and • the language that we use to reason about it.  ... 
doi:10.1613/jair.648 fatcat:gem3lkijqfhg5epzyj4cr7xt5y

A Theory of First-Order Counterfactual Reasoning [chapter]

Michael Thielscher
1999 Lecture Notes in Computer Science  
The assertion of a counterfactual antecedent is axiomatized as the performance of a special action.  ...  s characterization, based on causal models, of propositional counterfactuals.  ...  Σ * Circuit ∪ {(4)} is consistent with, Poss(S 0 ¡ On(Light) ∧ Denied (Switch-Light-Relation)) Axiomatizing Causal Model-Counterfactuals In concentrating on the crucial connection between reasoning about  ... 
doi:10.1007/3-540-48238-5_11 fatcat:h42kd7sk3nbmro4lvsfbvycdtu

Causal models have no complete axiomatic characterization [article]

Sanjiang Li
2008 arXiv   pre-print
This paper, however, shows that independencies captured by Bayesian networks (called causal models) have no axiomatization by using even countably many Horn or disjunctive clauses.  ...  This is because a sub-independency model of a causal model may be not causal, while graph-isomorphs are closed under sub-models.  ...  Causal models have no complete axiomatic characterization.Proof. Let Γ = {A 1 , A 2 , · · · } be the set of clauses that are satisfied by all causal models.  ... 
arXiv:0804.2401v1 fatcat:gascfy22qjeylnmamyrj6lbx64

Making use of logic

Max Urchs
2004 Logic and Logical Philosophy  
We take a closer look at the formalization of natural reasoning, inconsistency-tolerant logic, and at the formal analysis of causal nexus.  ...  Third, one of the very first axiomatic systems in causal logic was given by Henryk Greniewski in Greniewski 1925.  ...  But there is obviously a need for metamathematical counterparts of causal relations. For instance, robotics is desperately looking for reasonable causal simulators.  ... 
doi:10.12775/llp.1998.011 fatcat:parz6etwhvgnbebdkr5g4jbtbi

General Diagnostic Framework Based on Non-axiomatic Logic for Aviation Safety Event Analysis

Yang JIANG, Hong WANG, Xingjie FENG
2019 Chinese journal of electronics  
To achieve causality reasoning of aviation safety events based on big data of cross-media network, a data-driven general diagnostic framework based on nonaxiomatic logic is designed and implemented.  ...  On the basis of this framework, the uncertain causality between aviation safety events and faults is expressed in the form of binary non-axiomatic incident experience at first.  ...  In this paper, we design a data-driven general diagnostic framework based on non-axiomatic logic, which not only represents the uncertain causal relation between all faults and events in aviation safety  ... 
doi:10.1049/cje.2019.07.010 fatcat:pooir6ucd5dgnnow74sv4bkmcy

Psychological Explanation, Ontological Commitment and the Semantic View of Theories [chapter]

Colin Klein
2014 New Waves in Philosophy of Mind  
I do not focus on these formulations for two reasons.  ...  Rather, it is proportionality between higher-level cause and effect that picks out the most explanatory of the causally relevant properties.  ...  The idea that physics only describes mereological simples is almost unavoidable on the axiomatic view, for reasons outlined above.  ... 
doi:10.1057/9781137286734_10 fatcat:425nyt46sfartfixusaoagf3xq

Students' understanding of proofs: a historical analysis and implications for the teaching of geometry and linear algebra

Guershon Harel
1999 Linear Algebra and its Applications  
Axiomatizing.  ...  There really are three dierent levels of the axiomatic conception, which historically were developed in three consecutive periods: Intuitive axiomatic conception, structural conception, and axiomatizing  ... 
doi:10.1016/s0024-3795(99)00139-1 fatcat:qenvtyqcqrdrxebwwmp4fylyjm

Hilbert's 'Foundations of Physics': Gravitation and electromagnetism within the axiomatic method

K.A. Brading, T.A. Ryckman
2008 Studies in history and philosophy of modern physics  
stated was the case), and (b) the second contribution is a fine and coherent piece of work within this framework, whose principal aim is to address the apparent tension between general invariance and causality  ...  largely either disregarded or misinterpreted, and our aim is to show that (a) Hilbert's two contributions should be regarded as part of a wider research program within the overarching framework of "the axiomatic  ...  But the Mie theory also presented an eminently suitable candidate for the attention of the 'axiomatic method' for a number of other reasons that merit illumination, reasons not physical but mathematical  ... 
doi:10.1016/j.shpsb.2007.08.002 fatcat:3hmslb5vozh5xfyhpltpixhkqi

Applying causality principles to the axiomatization of probabilistic cellular automata [article]

Pablo Arrighi, Renan Fargetton, Vincent Nesme, Eric Thierry
2011 arXiv   pre-print
At least in the classical, reversible and quantum cases, these two top-down axiomatic conditions are sufficient to entail more bottom-up, operational descriptions of G.  ...  Further, this global evolution G is required to be shift-invariant (it acts the same everywhere) and causal (information cannot be transmitted faster than some fixed number of cells per time step).  ...  Then PCA will just be causal, shift-invariant stochastic maps. Continuity In the deterministic case CA were axiomatized by the celebrated Curtis-Lyndon-Hedlund Theorem [13] , which we now recall.  ... 
arXiv:1102.0860v2 fatcat:7uim22tdijcixe3aut47jmbzhy

Probabilistic Reasoning Across the Causal Hierarchy

Duligur Ibeling, Thomas Icard
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
do-calculus reasoning for causal effects, and the third capturing a fully expressive do-calculus for arbitrary counterfactual queries.  ...  We give a corresponding series of finitary axiomatizations complete over both structural causal models and probabilistic programs, and show that satisfiability and validity for each language are decidable  ...  In possession of a precise syntax and semantics for probabilistic causal reasoning, questions of axiomatization naturally arise.  ... 
doi:10.1609/aaai.v34i06.6577 fatcat:mmu64kwb4zfkxahiq7site3b2a

OntoTimeFL – A Formalism for Temporal Annotation and Reasoning for Natural Language Text [chapter]

Francesco Mele, Antonio Sorgente
2013 Studies in Computational Intelligence  
OntoTimeFL entities have been defined as classes of a formal ontology; a methodological choice for facilitating automatic annotation processes to reuse existing axiomatics in the research of temporal reasoning  ...  In addition, OntoTimeFL introduces new constructs for the annotation that mainly concern three complex events: narrative, intentional, and causal.  ...  With this representation then, one can annotate causal relations and associate rules (axioms) for their causal reasoning.  ... 
doi:10.1007/978-3-642-31546-6_9 fatcat:funloxanefhadgwmxk4asdkkuq

Probabilistic Reasoning across the Causal Hierarchy [article]

Duligur Ibeling, Thomas Icard
2021 arXiv   pre-print
do-calculus reasoning for causal effects, and the third capturing a fully expressive do-calculus for arbitrary counterfactual queries.  ...  We give a corresponding series of finitary axiomatizations complete over both structural causal models and probabilistic programs, and show that satisfiability and validity for each language are decidable  ...  In possession of a precise syntax and semantics for probabilistic causal reasoning, questions of axiomatization naturally arise.  ... 
arXiv:2001.02889v5 fatcat:y35w6gyjybhsnevhujmlzieju4

An Axiomatic Semantics for the Synchronous Language Gentzen [chapter]

Simone Tini
2001 Lecture Notes in Computer Science  
We propose an axiomatic semantics for the synchronous language Gentzen, which is an instantiation of the paradigm Timed Concurrent Constraint Programming.  ...  Since synchronous concurrency cannot be simulated by arbitrary interleaving, we cannot exploit "head normal forms", on which axiomatic theories for asynchronous process calculi are based.  ...  As an example, it could seem to be reasonable to remove N l1 and to add the causality term ({a}, s) to E l1 , with s denoting some idle action.  ... 
doi:10.1007/3-540-45315-6_26 fatcat:44zxbi6vyrdvbjztmwczcaxhvm
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