Grounding Possible Worlds Semantics in Experiential Semantics

Lecture Notes in Computer Science, 2004

In this paper we consider a logic programming framework for reasoning about imprecise probabilities. In particular, we propose a new semantics, for the Probabilistic Logic Programs (p-programs) of Ng and Subrahmanian. Pprograms represent imprecision using probability intervals. Our semantics, based on the possible worlds semantics, considers all point probability distributions that satisfy a given p-program. In the paper, we provide the exact characterization of such models of a p-program. We show that the set of models of a p-program cannot, in general case, be described by single intervals associated with atoms of the program. We provide algorithms for efficient construction of this set of models and study their complexity.

Discrete Applied Mathematics, 1992

Directed Agent) is a model for autonomous learning in probabilistic domains [desJ ardins,

International Journal of Approximate Reasoning, 2008

Logical formalisation of agent behaviour is desirable, not only in order to provide a clear semantics of agent-based systems, but also to provide the foundation for sophisticated reasoning techniques to be used on, and by, the agents themselves. The possible worlds semantics offered by modal logic has proved to be a successful framework in which to model mental attitudes of agents such as beliefs, desires and intentions. The most popular choices for modeling the informational attitudes involves annotating the agent with an S5-like logic for knowledge, or a KD45-like logic for belief. However, using these logics in their standard form, an agent cannot distinguish situations in which the evidence for a certain fact is 'equally distributed' over its alternatives, from situations in which there is only one, almost negligible, counterexample to a 'fact'. Probabilistic modal logics are a way to address this, but they easily end up being both computationally and conceptually complex, for example often lacking the property of compactness. In this paper, we propose a probabilistic modal logic P F KD45, in which the probabilities of the possible worlds range over a finite domain of values, while still allowing the agent to reason about infinitely many options. In this way, the logic remains compact, implying that the agent still has to consider only finitely many possibilities for probability distributions during a reasoning task. We demonstrate a sound, compact and complete axiomatization for P F KD45 and show that it has several appealing features. Then, we discuss an implemented decision procedure for the logic, and provide a small example.

Strict preservation of the (minimum of the) premise probabilities under all (even 'abnormal') probability distributions P loosens this Z and QC loosen also this Strict probability semantics:

Advances in Soft Computing, 2008

This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular semantics, no general solution is possible. The paper discusses several possible semantics by looking at it from the perspective of probabilistic argumentation.

This paper concerns building probabilistic models with an underlying ontology that defines the classes and properties used in the model. In particular, it considers the problem of reasoning with properties that may not always be defined. Furthermore, we may even be uncertain about whether a property is defined for a given individual. One approach is to explicitly add a value "undefined" to the range of random variables, forming extended belief networks; however, adding an extra value to a random variable's range has a large computational overhead. In this paper, we propose an alternative, ontologically-based belief networks, where all properties are only used when they are defined, and we show how probabilistic reasoning can be carried out without explicitly using the value "undefined" during inference. We prove this is equivalent to reasoning with the corresponding extended belief network and empirically demonstrate that inference becomes more efficient.

2013

A framework is presented for a computational theory of probabilistic argument. The Probabilistic Reasoning Environment encodes knowledge at three levels. At the deepest level are a set of schemata encoding the system's domain knowledge. This knowledge is used to build a set of second-level arguments, which are structured for efficient recapture of the knowledge used to construct them. Finally, at the top level is a Bayesian network constructed from the arguments. The system is designed to facilitate not just propagation of beliefs and assimilation of evidence, but also the dynamic process of constructing a belief network, evaluating its adequacy, and revising it when necessary.

Lecture Notes in Computer Science, 2004

Logical formalisation of agent behaviour is desirable, not only in order to provide a clear semantics of agent-based systems, but also to provide the foundation for sophisticated reasoning techniques to be used on, and by, the agents themselves. The possible worlds semantics offered by modal logic has proved to be a successful framework in which to model mental attitudes of agents such as beliefs, desires and intentions. The most popular choices for modeling the informational attitudes involves annotating the agent with an S5 -like logic for knowledge, or a KD45 -like logic for belief. However, using these logics in their standard form, an agent cannot distinguish situations in which the evidence for a certain fact is 'equally distributed' over its alternatives, from situations in which there is only one, almost negligible, counterexample to the 'fact'. Probabilistic modal logics are a way to address this, but they easily end up being both computationally and conceptually complex, for example often lacking the property of compactness. In this paper, we propose a probabilistic modal logic PF KD45 , in which the probabilities of the possible worlds range over a finite domain of values, while still allowing the agent to reason about infinitely many options. In this way, the logic remains compact, implying that the agent still has to consider only finitely many possibilities for probability distributions during a reasoning task. We demonstrate a sound, compact and complete axiomatisation for PF KD45 and show that it has several appealing features. Then, we discuss an implemented decision procedure for the logic, and provide a small example. Finally we show that, rather than specifying them beforehand, the finite set of possible probabilities can be obtained directly from the problem specification.

Although probabilistic knowledge representations and probabilistic reasoning have by now secured their position in intelligent systems research, it is not uncommon to encounter misunderstanding of their foundations and lack of appreciation for their strengths. This paper discusses ve issues related to intelligent systems research and shows how they are addressed by the probabilistic knowledge representations. Directed probabilistic graphs capture essential qualitative properties of a domain, along with its causal structure. Concepts such as relevance and con icting evidence have a natural, formally sound meaning in probabilistic models. Probabilistic schemes support sound reasoning at a variety of levels ranging from purely quantitative to purely qualitative levels. Probabilistic knowledge representations provide insight into the foundations of logic-based schemes for reasoning under uncertainty, showing their di culties in highly uncertain domains. Finally, probabilistic knowledge representations support automatic generation of understandable explanations of inference for the sake of user interfaces to intelligent systems.

Fundamenta Informaticae

Although probabilistic knowledge representations and probabilistic reasoning have by now secured their position in arti cial intelligence, it is not uncommon to encounter misunderstanding of their foundations and lack of appreciation for their strengths. This paper describes ve properties of probabilistic knowledge representations that are particularly useful in intelligent systems research. (1) Directed probabilistic graphs capture essential qualitative properties of a domain, along with its causal structure. (2) Concepts such as relevance and con icting evidence have a natural, formally sound meaning in probabilistic models. (3) Probabilistic schemes support sound reasoning at a variety of levels ranging from purely quantitative to purely qualitative levels. (4) The role of probability theory in reasoning under uncertainty can be compared to the role of rst order logic in reasoning under certainty. Probabilistic knowledge representations provide insight into the foundations of logic-based schemes, showing their di culties in highly uncertain domains. Finally, (5) probabilistic knowledge representations support automatic generation of understandable explanations of inference for the sake of user interfaces to intelligent systems.