Horn axiomatizations for sequential data

AbstractWe propose a notion of deterministic association rules for ordered data. We prove that our proposed rules can be formally justified by a purely logical characterization, namely, a natural notion of empirical Horn approximation for ordered data which involves background Horn conditions; these ensure the consistency of the propositional theory obtained with the ordered context. The whole framework resorts to concept lattice models from Formal Concept Analysis, but adapted to ordered contexts. We also discuss a general method to mine these rules that can be easily incorporated into any algorithm for mining closed sequences, of which there are already some in the literature

On mining complex sequential data by means of FCA and pattern structures

Nowadays data sets are available in very complex and heterogeneous ways. Mining of such data collections is essential to support many real-world applications ranging from healthcare to marketing. In this work, we focus on the analysis of "complex" sequential data by means of interesting sequential patterns. We approach the problem using the elegant mathematical framework of Formal Concept Analysis (FCA) and its extension based on "pattern structures". Pattern structures are used for mining complex data (such as sequences or graphs) and are based on a subsumption operation, which in our case is defined with respect to the partial order on sequences. We show how pattern structures along with projections (i.e., a data reduction of sequential structures), are able to enumerate more meaningful patterns and increase the computing efficiency of the approach. Finally, we show the applicability of the presented method for discovering and analyzing interesting patient patterns from a French healthcare data set on cancer. The quantitative and qualitative results (with annotations and analysis from a physician) are reported in this use case which is the main motivation for this work. Keywords: data mining; formal concept analysis; pattern structures; projections; sequences; sequential data.Comment: An accepted publication in International Journal of General Systems. The paper is created in the wake of the conference on Concept Lattice and their Applications (CLA'2013). 27 pages, 9 figures, 3 table

A Denotational Semantics for First-Order Logic

In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic. Additionally, by allowing an assignment of a non-ground term to a variable we introduce in this framework logical variables. The semantics combines a number of well-known ideas from the areas of semantics of imperative programming languages and logic programming. In the resulting computational view conjunction corresponds to sequential composition, disjunction to ``don't know'' nondeterminism, existential quantification to declaration of a local variable, and negation to the ``negation as finite failure'' rule. The soundness result shows correctness of the semantics with respect to the notion of truth. The proof resembles in some aspects the proof of the soundness of the SLDNF-resolution.Comment: 17 pages. Invited talk at the Computational Logic Conference (CL 2000). To appear in Springer-Verlag Lecture Notes in Computer Scienc

Qualitative Reasoning on Complex Systems from Observations

A hybrid approach to phenomenological reconstruction of Complex Systems (CS), using Formal Concept Analysis (FCA) as main tool for conceptual data mining, is proposed. To illustrate the method, a classic CS is selected (cellular automata), to show how FCA can assist to predict CS evolution under different conceptual descriptions (from different observable features of the CS).Junta de Andalucía TIC-606

Action Logic Programs: How to Specify Strategic Behavior in Dynamic Domains Using Logical Rules

We discuss a new concept of agent programs that combines logic programming with reasoning about actions. These agent logic programs are characterized by a clear separation between the specification of the agent’s strategic behavior and the underlying theory about the agent’s actions and their effects. This makes it a generic, declarative agent programming language, which can be combined with an action representation formalism of one’s choice. We present a declarative semantics for agent logic programs along with (two versions of) a sound and complete operational semantics, which combines the standard inference mechanisms for (constraint) logic programs with reasoning about actions

Security and Modularity in Message Passing

This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's artificial intelligence research is provided in part by the Office of Naval Research of the Department of Defense under contract N00014-75-C-0522.This paper addresses theoretical issues involved for the implementation of security and modularity in concurrent systems. It explicates the theory behind a mechanism for safely delegating messages to shared handlers in order to increase the modularity of concurrent systems. Our mechanism has the property that the actions caused by delegated messages are atomic. That is the handling of a message delegated by a client actor appears to be indivisible to other users of the actor. Our mechanism for delegating communications is a generalization suitable for use in concurrent systems of the sub-class mechanism of SIMULA. Our mechanism has the benefit that it easily lends itself to the implementation of efficient flexible access control mechanisms in distributed systems. It is a generalization of the protection mechanisms provided by capability-based system, access control lists, and the access control mechanisms provided by PDP-10 SIMULA.MIT Artificial Intelligence Laboratory Department of Defense Office of Naval Researc

Synthetizing Qualitative (Logical) Patterns for Pedestrian Simulation from Data

This work introduces a (qualitative) data-driven framework to extract patterns of pedestrian behaviour and synthesize Agent-Based Models. The idea consists in obtaining a rule-based model of pedestrian behaviour by means of automated methods from data mining. In order to extract qualitative rules from data, a mathematical theory called Formal Concept Analysis (FCA) is used. FCA also provides tools for implicational reasoning, which facilitates the design of qualitative simulations from both, observations and other models of pedestrian mobility. The robustness of the method on a general agent-based setting of movable agents within a grid is shown.Ministerio de Economía y Competitividad TIN2013-41086-