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Studies in Logic, Grammar and Rhetoric
Reasoning is not just following logical rules, but a large part of human reasoning depends on our expectations about the world. To some extent, non-monotonic logic has been developed to account for the role of expectations. In this article, the focus is on expectations based on actions and their consequences. The analysis is based on a two-vector model of events where an event is represented in terms of two main components – the force of an action that drives the event, and the result of its application. Actions are modelled in terms of the force domain and the results are modelled with the aid of different domains for locations or properties of objects. As a consequence, the assumption that reasoning about causal relations should be made in terms of propositional structures becomes very unnatural. Instead, the reasoning will be based on the geometric and topological properties of causes and effects modelled in conceptual spaces.
Frontiers in Psychology
The aim of the article is to present a model of causal relations that is based on what is known about human causal reasoning and that forms guidelines for implementations in robots. I argue for two theses concerning human cognition. The first is that human causal cognition, in contrast to that of other animals, is based on the understanding of the forces that are involved. The second thesis is that humans think about causality in terms of events. I present a two-vector model of events, developed by Gärdenfors and Warglien, which states that an event is represented in terms of two main componentsthe force of an action that drives the event, and the result of its application. Apart from the causal mapping, the event model contains representations of a patient, an agent, and possibly some other roles. Agents and patients are objects (animate or inanimate) that have different properties. Following my theory of conceptual spaces, they can be described as vectors of property values. At least two spaces are needed to describe an event, an action space and a result space. The result of an event is modeled as a vector representing the change of properties of the patient before and after the event. In robotics the focus has been on describing results. The proposed model also includes the causal part of events, typically described as an action. A central part of an event category is the mapping from actions to results. This mapping contains the central information about causal relations. In applications of the two-vector model, the central problem is how the event mapping can be learned in a way that is amenable to implementations in robots. Three processes are central for event cognition: causal thinking, control of action and learning by generalization. Although it is not yet clear which is the best way to model how the mappings can be learned, they should be constrained by three corresponding mathematical properties: monotonicity (related to qualitative causal thinking); continuity (plays a key role in activities of action control); and convexity (facilitates generalization and the categorization of events). I argue that Bayesian models are not suitable for these purposes, but some more geometrically oriented approach to event mappings should be used.
Proceedings of the 18th International Joint Conference on Artificial Intelligence, 2003
We introduce a logical formalism of irreflexivc causal production relations that possesses both a standard monotonic semantics, and a natural nonmonotonic semantics. The formalism is shown to provide a complete characterization for the causal reasoning behind causal theories from [McCain and Turner, 1997]. It is shown also that any causal relation is reducible to its Horn sub-relation with respect to the nonmonotonic semantics. We describe also a general correspondence between causal relations and abductive systems, which shows, in effect, that causal relations allow to express abductive reasoning. The results of the study seem to suggest causal production relations as a viable general framework for nonmonotonic reasoning.
Causal composition allows people to generate new causal relations by combining existing causal knowledge. We introduce a new computational model of such reasoning, the force theory, which holds that people compose causal relations by simulating the processes that join forces in the world, and compare this theory with the mental model theory (Khemlani et al., 2014) and the causal model theory (Sloman et al., 2009), which explain causal composition on the basis of mental models and structural equations, respectively. In one experiment, the force theory was uniquely able to account for people's ability to compose causal relationships from complex animations of real-world events. In three additional experiments, the force theory did as well as or better than the other two theories in explaining the causal compositions people generated from linguistically presented causal relations. Implications for causal learning and the hierarchical structure of causal knowledge are discussed.
Principles of Knowledge Representation and Reasoning, 2016
We will explore the use of disjunctive causal rules for representing indeterminate causation. We provide first a logical formalization of such rules in the form of a disjunctive inference relation, and describe its logical semantics. Then we consider a nonmonotonic semantics for such rules, described in (Turner 1999). It will be shown, however, that, under this semantics, disjunctive causal rules admit a stronger logic in which these rules are reducible to ordinary, singular causal rules. This semantics also tends to give an exclusive interpretation of disjunctive causal effects, and so excludes some reasonable models in particular cases. To overcome these shortcomings, we will introduce an alternative nonmonotonic semantics for disjunctive causal rules, called a covering semantics, that permits an inclusive interpretation of indeterminate causal information. Still, it will be shown that even in this case there exists a systematic procedure, that we will call a normalization, that allows us to capture precisely the covering semantics using only singular causal rules. This normalization procedure can be viewed as a kind of nonmonotonic completion, and it generalizes established ways of representing indeterminate effects in current theories of action.
We introduce logical formalisms of production and causal inference relations based on input/output logics of (Makinson and van der Torre, 2000). These inference relations are assigned, however, both standard monotonic semantics, and natural nonmonotonic semantics based on the principle of explanatory closure. The resulting nonmonotonic for- malisms will be shown to provide a logical representation of abductive reasoning, and a complete characterization of causal nonmonotonic reasoning from (McCain and Turner, 1997). The results of the study suggest production and causal inference as a new general framework for nonmonotonic reasoning.
Lecture Notes in Computer Science
This paper proposes a formal framework for modeling the interaction of causal and (qualitative) epistemic reasoning. To this purpose, we extend the notion of a causal model [16, 17, 26, 11] with a representation of the epistemic state of an agent. On the side of the object language, we add operators to express knowledge and the act of observing new information. We provide a sound and complete axiomatization of the logic, and discuss the relation of this framework to causal team semantics.
Lecture Notes in Computer Science, 1999
A unifying semantic framework for different reasoning approaches provides an ideal tool to compare these competing alternatives. A historic example is Kripke's possible world semantics that provided a unifying framework for different systems of modal logic. More recently, Shoham's work on preferential semantics similarly provided a much needed framework to uniformly represent and compare a variety of nonmonotonic logics (including some logics of action). The present work develops a novel type of semantics for a particular causal approach to reasoning about action. The basic idea is to abandon the standard state-space of possible worlds and consider instead a larger set of possibilities -a hyper-space -tracing the effects of actions (including indirect effects) with the states in the hyper-space. Intuitively, the purpose of these hyper-states is to supply extra context to record the process of causality.
International Joint Conference on Artificial Intelligence, 2001
We consider the problem of how an agent creates a discrete spatial representation from its continuous interactions with the environment. Such represen- tation will be the minimal one that explains the ex- periences of the agent in the environment. In this paper we take the Spatial Semantic Hierarchy as the agent's target spatial representation, and use a circumscriptive theory to
2012
Despite their success in transferring the powerful human faculty of causal reasoning to a mathematical and computational form, causal models have not been widely used in the context of core AI applications such as robotics. In this paper, we argue that this discrepancy is due to the static, propositional nature of existing causality formalisms that make them difficult to apply in dynamic real-world situations where the variables of interest are not necessarily known a priori. We define Causal Logic Models (CLMs), a new probabilistic, first-order representation which uses causality as a fundamental building block. Rather than merely converting causal rules to first-order logic as various methods in Statistical Relational Learning have done, we treat the causal rules as basic primitives which cannot be altered without changing the system. We provide sketches of algorithms for causal reasoning using CLMs, preliminary results for causal explanation, and explore the significant differenc...
Artificial Intelligence, 2004
In this paper we present a new approach to reasoning about actions and causation which is based on a conditional logic. The conditional implication is interpreted as causal implication. This makes it possible to formalize in a uniform way causal dependencies between actions and their immediate and indirect effects. The proposed approach also provides a natural formalization of concurrent actions and of the dependency (and independency) relations between actions. The properties of causality are formalized as axioms of the conditional connectives and a nonmonotonic (abductive) semantics is adopted for dealing with the frame problem.
According to the transitive dynamics model, people can construct causal structures by linking together configurations of force. The predictions of the model were tested in two experiments in which participants generated new causal relationships by chaining together two (Experiment 1) or three (Experiment 2) causal relations. The predictions of the transitive dynamics model were compared against those of Goldvarg and Johnson-Laird's model theory . The transitive dynamics model consistently predicted the overall causal relationship drawn by participants for both types of causal chains, and, when compared to the model theory, provided a better fit to the data. The results suggest that certain kinds of causal reasoning may depend on force dynamic-rather than on purely logical or statistical-representations.
2018
We explore the relationships between causal rules and counterfactuals, as well as their relative representation capabilities, in the logical framework of the causal calculus. It will be shown that, though counterfactuals are readily definable on the basis of causal rules, the reverse reduction is achievable only up to a certain logical threshold (basic equivalence). As a result, we will argue that counterfactuals cannot distinguish causal theories that justify different claims of actual causation, which could be seen as the main source of the problem of ‘structural equivalents’ in counterfactual approaches to causation. This will lead us to a general conclusion about the primary role of causal rules in representing causation.
1988
In this paper we describe a problem-solving system which uses a multi-level causal model of its domain. The system functions in the role of a pilot's assistant in the domain of commercial air transport emergencies. The model represents causal relationships among the aircraft subsystems, the effectors (engines, control surfaces), the forces that act on an aircraft in flight (thrust, lift), and the aircraft's flight profile (speed, .altitude, etc.). The causal relationsllips are represented at three levels of abstraction: Boolean, qualitative, and quantitative, and reasoning about causes and effects can rake place at each of these levels. Since processing at each level has different characteristics with respect to speed, the type of data required, and the specificity of the results, the problem-solving system can adapt to a wide variety of situations. The system is currently being implemented in the KEE TM development environment on a Symbolics Lisp machine.
Studia Logica, 2004
The McCain-Turner semantics of causal rules is based on a xpoint construction similar to the one found in the de nition of default logic. In the special case when the heads of the rules are literals, it can be equivalently expressed by a translation from sets of rules into sets of propositional formulas. In this note, we de ne a translation from causal logic into classical logic that characterizes the semantics of arbitrary causal rules, without any restrictions on their syntactic form. This translation suggests a way to extend the McCain-Turner logic to nonpropositional causal theories. 1 The syntax used in is G ) F. 1997b], literal completion is used to apply satis ability planning Kautz and Selman, 1992] to action domains described by causal theories.
This paper proposes a new model of causal meaning, the Vector Model, which formalizes a model of causation based on Talmys notions of force dynamics (Wolff, Song, & Driscoll, 2002). In the Vector Model, the concepts of CAUSE, ENABLE and PREVENT are distinguished from one another in terms of force vectors, their resultant and the relationship of each force vector to a target vector. The predictions of the model were tested in two experiments in which participants saw realistic 3D-animations of an inflatable boat moving through a pool of water. The boats movements were completely determined by the force vectors entered into a physics simulator. Participants linguistic descriptions of the animations were closely matched by those predicted by the model given the same force vectors as those used to produce the animations. Our model may have implications for the semantics of causal verbs as well as the perception of causal events.
Theory and Practice of Logic Programming, 2009
We examine the relation between constructive processes and the concept of causality. We observe that causality has an inherent dynamic aspect, i.e., that, in essence, causal information concerns the evolution of a domain over time. Motivated by this observation, we construct a new representation language for causal knowledge, whose semantics is defined explicitly in terms of constructive processes. This is done in a probabilistic context, where the basic steps that make up the process are allowed to have non-deterministic effects. We then show that a theory in this language defines a unique probability distribution over the possible outcomes of such a process. This result offers an appealing explanation for the usefulness of causal information and links our explicitly dynamic approach to more static causal probabilistic modeling languages, such as Bayesian networks. We also show that this language, which we have constructed to be a natural formalization of a certain kind of causal statements, is closely related to logic programming. This result demonstrates that, under an appropriate formal semantics, a rule of a normal, a disjunctive or a certain kind of probabilistic logic program can be interpreted as a description of a causal event. * Research supported by GOA 2003/8 Inductive Knowledge Bases and by FWO Vlaanderen. † Joost Vennekens is a postdoctoral researcher of the FWO.
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