Hybrid type theory: a quartet in four movements

This paper sings a song -a song created by bringing together the work of four great names in the history of logic: Hans Reichenbach, Arthur Prior, Richard Montague, and Leon Henkin. Although the work of the first three of these authors have previously been combined, adding the ideas of Leon Henkin is the addition required to make the combination work at the logical level. But the present paper does not focus on the underlying technicalities (these can be found in Areces, Blackburn, Huertas, and Manzano [to appear]) rather it focusses on the underlying instruments, and the way they work together. We hope the reader will be tempted to sing along

Reasoning About a Simulated Printer Case Investigation with Forensic Lucid

In this work we model the ACME (a fictitious company name) "printer case incident" and make its specification in Forensic Lucid, a Lucid- and intensional-logic-based programming language for cyberforensic analysis and event reconstruction specification. The printer case involves a dispute between two parties that was previously solved using the finite-state automata (FSA) approach, and is now re-done in a more usable way in Forensic Lucid. Our simulation is based on the said case modeling by encoding concepts like evidence and the related witness accounts as an evidential statement context in a Forensic Lucid program, which is an input to the transition function that models the possible deductions in the case. We then invoke the transition function (actually its reverse) with the evidential statement context to see if the evidence we encoded agrees with one's claims and then attempt to reconstruct the sequence of events that may explain the claim or disprove it.Comment: 18 pages, 3 figures, 7 listings, TOC, index; this article closely relates to arXiv:0906.0049 and arXiv:0904.3789 but to remain stand-alone repeats some of the background and introductory content; abstract presented at HSC'09 and the full updated paper at ICDF2C'11. This is an updated/edited version after ICDF2C proceedings with more references and correction

The Need to Support of Data Flow Graph Visualization of Forensic Lucid Programs, Forensic Evidence, and their Evaluation by GIPSY

Lucid programs are data-flow programs and can be visually represented as data flow graphs (DFGs) and composed visually. Forensic Lucid, a Lucid dialect, is a language to specify and reason about cyberforensic cases. It includes the encoding of the evidence (representing the context of evaluation) and the crime scene modeling in order to validate claims against the model and perform event reconstruction, potentially within large swaths of digital evidence. To aid investigators to model the scene and evaluate it, instead of typing a Forensic Lucid program, we propose to expand the design and implementation of the Lucid DFG programming onto Forensic Lucid case modeling and specification to enhance the usability of the language and the system and its behavior. We briefly discuss the related work on visual programming an DFG modeling in an attempt to define and select one approach or a composition of approaches for Forensic Lucid based on various criteria such as previous implementation, wide use, formal backing in terms of semantics and translation. In the end, we solicit the readers' constructive, opinions, feedback, comments, and recommendations within the context of this short discussion.Comment: 11 pages, 7 figures, index; extended abstract presented at VizSec'10 at http://www.vizsec2010.org/posters ; short paper accepted at PST'1

Advances in the Design and Implementation of a Multi-Tier Architecture in the GIPSY Environment

We present advances in the software engineering design and implementation of the multi-tier run-time system for the General Intensional Programming System (GIPSY) by further unifying the distributed technologies used to implement the Demand Migration Framework (DMF) in order to streamline distributed execution of hybrid intensional-imperative programs using Java.Comment: 11 pages, 3 figure

A Goal-Directed Implementation of Query Answering for Hybrid MKNF Knowledge Bases

Ontologies and rules are usually loosely coupled in knowledge representation formalisms. In fact, ontologies use open-world reasoning while the leading semantics for rules use non-monotonic, closed-world reasoning. One exception is the tightly-coupled framework of Minimal Knowledge and Negation as Failure (MKNF), which allows statements about individuals to be jointly derived via entailment from an ontology and inferences from rules. Nonetheless, the practical usefulness of MKNF has not always been clear, although recent work has formalized a general resolution-based method for querying MKNF when rules are taken to have the well-founded semantics, and the ontology is modeled by a general oracle. That work leaves open what algorithms should be used to relate the entailments of the ontology and the inferences of rules. In this paper we provide such algorithms, and describe the implementation of a query-driven system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic) rules under the well-founded semantics and a (monotonic) ontology, represented by a CDF Type-1 (ALQ) theory. To appear in Theory and Practice of Logic Programming (TPLP

Formally Specifying and Proving Operational Aspects of Forensic Lucid in Isabelle

A Forensic Lucid intensional programming language has been proposed for intensional cyberforensic analysis. In large part, the language is based on various predecessor and codecessor Lucid dialects bound by the higher-order intensional logic (HOIL) that is behind them. This work formally specifies the operational aspects of the Forensic Lucid language and compiles a theory of its constructs using Isabelle, a proof assistant system.Comment: 23 pages, 3 listings, 3 figures, 1 table, 1 Appendix with theorems, pp. 76--98. TPHOLs 2008 Emerging Trends Proceedings, August 18-21, Montreal, Canada. Editors: Otmane Ait Mohamed and Cesar Munoz and Sofiene Tahar. The individual paper's PDF is at http://users.encs.concordia.ca/~tphols08/TPHOLs2008/ET/76-98.pd