Multi-agent Confidential Abductive Reasoning

In the context of multi-agent hypothetical reasoning, agents typically have partial knowledge about their environments, and the union of such knowledge is still incomplete to represent the whole world. Thus, given a global query they collaborate with each other to make correct inferences and hypothesis, whilst maintaining global constraints. Most collaborative reasoning systems operate on the assumption that agents can share or communicate any information they have. However, in application domains like multi-agent systems for healthcare or distributed software agents for security policies in coalition networks, confidentiality of knowledge is an additional primary concern. These agents are required to collaborately compute consistent answers for a query whilst preserving their own private information. This paper addresses this issue showing how this dichotomy between "open communication" in collaborative reasoning and protection of confidentiality can be accommodated. We present a general-purpose distributed abductive logic programming system for multi-agent hypothetical reasoning with confidentiality. Specifically, the system computes consistent conditional answers for a query over a set of distributed normal logic programs with possibly unbound domains and arithmetic constraints, preserving the private information within the logic programs. A case study on security policy analysis in distributed coalition networks is described, as an example of many applications of this system

Proceedings of the Workshop on the lambda-Prolog Programming Language

The expressiveness of logic programs can be greatly increased over first-order Horn clauses through a stronger emphasis on logical connectives and by admitting various forms of higher-order quantification. The logic of hereditary Harrop formulas and the notion of uniform proof have been developed to provide a foundation for more expressive logic programming languages. The λ-Prolog language is actively being developed on top of these foundational considerations. The rich logical foundations of λ-Prolog provides it with declarative approaches to modular programming, hypothetical reasoning, higher-order programming, polymorphic typing, and meta-programming. These aspects of λ-Prolog have made it valuable as a higher-level language for the specification and implementation of programs in numerous areas, including natural language, automated reasoning, program transformation, and databases

Abductive reasoning in neural-symbolic learning systems

Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested in benefiting from developments made by each community. In particular, we are interested in the ability of non-symbolic systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both approaches employ standard neural network architectures which are already known to be highly effective in practical learning applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning, while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world. Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective of symbolic and sub-symbolic integration

Epistemic Modals in Hypothetical Reasoning

Data involving epistemic modals suggest that some classically valid argument forms, such as reductio, are invalid in natural language reasoning as they lead to modal collapses. We adduce further data showing that the classical argument forms governing the existential quantifier are similarly defective, as they lead to a de re–de dicto collapse. We observe a similar problem for disjunction. But if the classical argument forms for negation, disjunction and existential quantification are invalid, what are the correct forms that govern the use of these items? Our diagnosis is that epistemic modals interfere with hypothetical reasoning. We present a modal first-order logic and model theory that characterizes hypothetical reasoning with epistemic modals in a principled manner. One upshot is a sound and complete natural deduction system for reasoning with epistemic modals in first-order logic.</p

Geological Multi-scenario Reasoning

In the oil and gas industry, during exploration prospect assessment, explorationists rely on ad hoc manual work practices and tools for developing and communicating multiple hypothetical geological scenarios of the prospect. This leaves them with little efficient means to make the fullest use of state of the art digital technologies to communicate and systematically compare and assess different hypothetical geological scenarios before deciding which scenario to pursue. In this paper, we present a formal framework for geological multi-scenario reasoning, a novel tool-based method for geologically oriented subsurface evaluation. The methodology applies formal methods and logic-based techniques to subsurface evaluation and expresses interpretive uncertainty as discrete scenarios with branches of potential alternatives. This framework consists of (i) a proto-scenario generator that takes user observations and geological evidence as input and generates semantically valid initial states based on formalized geological knowledge in first-order logic (ii) geological processes formalized as a rewrite theory that are executable in Maude. By applying geological rewrite rules onto the proto-scenarios, we are able to assist explorationists with multi-scenario generation and reasoning beyond human capacity

On abduction and answer generation through constrained resolution

Recently, extensions of constrained logic programming and constrained resolution for theorem proving have been introduced, that consider constraints, which are interpreted under an open world assumption. We discuss relationships between applications of these approaches for query answering in knowledge base systems on the one hand and abduction-based hypothetical reasoning on the other hand. We show both that constrained resolution can be used as an operationalization of (some limited form of) abduction and that abduction is the logical status of an answer generation process through constrained resolution, ie., it is an abductive but not a deductive form of reasoning

Distributed Abductive Reasoning: Theory, Implementation and Application

Abductive reasoning is a powerful logic inference mechanism that allows assumptions to be made during answer computation for a query, and thus is suitable for reasoning over incomplete knowledge. Multi-agent hypothetical reasoning is the application of abduction in a distributed setting, where each computational agent has its local knowledge representing partial world and the union of all agents' knowledge is still incomplete. It is different from simple distributed query processing because the assumptions made by the agents must also be consistent with global constraints. Multi-agent hypothetical reasoning has many potential applications, such as collaborative planning and scheduling, distributed diagnosis and cognitive perception. Many of these applications require the representation of arithmetic constraints in their problem specifications as well as constraint satisfaction support during the computation. In addition, some applications may have confidentiality concerns as restrictions on the information that can be exchanged between the agents during their collaboration. Although a limited number of distributed abductive systems have been developed, none of them is generic enough to support the above requirements. In this thesis we develop, in the spirit of Logic Programming, a generic and extensible distributed abductive system that has the potential to target a wide range of distributed problem solving applications. The underlying distributed inference algorithm incorporates constraint satisfaction and allows non-ground conditional answers to be computed. Its soundness and completeness have been proved. The algorithm is customisable in that different inference and coordination strategies (such as goal selection and agent selection strategies) can be adopted while maintaining correctness. A customisation that supports confidentiality during problem solving has been developed, and is used in application domains such as distributed security policy analysis. Finally, for evaluation purposes, a flexible experimental environment has been built for automatically generating different classes of distributed abductive constraint logic programs. This environment has been used to conduct empirical investigation of the performance of the customised system