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

Productivity of Stream Definitions

We give an algorithm for deciding productivity of a large and natural class of recursive stream definitions. A stream definition is called ‘productive’ if it can be evaluated continuously in such a way that a uniquely determined stream is obtained as the limit. Whereas productivity is undecidable for stream definitions in general, we show that it can be decided for ‘pure’ stream definitions. For every pure stream definition the process of its evaluation can be modelled by the dataflow of abstract stream elements, called ‘pebbles’, in a finite ‘pebbleflow net(work)’. And the production of a pebbleflow net associated with a pure stream definition, that is, the amount of pebbles the net is able to produce at its output port, can be calculated by reducing nets to trivial nets

Coeffects: Unified static analysis of context-dependence

Monadic effect systems provide a unified way of tracking effects of computations, but there is no unified mechanism for tracking how computations rely on the environment in which they are executed. This is becoming an important problem for modern software – we need to track where distributed computations run, which resources a program uses and how they use other capabilities of the environment. We consider three examples of context-dependence analysis: liveness analysis, tracking the use of implicit parameters (similar to tracking of resource usage in distributed computation), and calculating caching requirements for dataflow programs. Informed by these cases, we present a unified calculus for tracking context dependence in functional languages together with a categorical semantics based on indexed comonads. We believe that indexed comonads are the right foundation for constructing context-aware languages and type systems and that following an approach akin to monads can lead to a widespread use of the concept

Minimum model semantics for logic programs with negation-as-failure

We give a purely model-theoretic characterization of the semantics of logic programs with negationas-failure allowed in clause bodies. In our semantics, the meaning of a program is, as in the classical case, the unique minimum model in a program-independent ordering. We use an expanded truth domain that has an uncountable linearly ordered set of truth values between False (the minimum element) and True (the maximum), with a Zero element in the middle. The truth values below Zero are ordered like the countable ordinals. The values above Zero have exactly the reverse order. Negation is interpreted as reflection about Zero followed by a step towards Zero; the only truth value that remains unaffected by negation is Zero. We show that every program has a unique minimum model M P, and that this model can be constructed with a T P iteration which proceeds through the countable ordinals. Furthermore, we demonstrate that M P can alternatively be obtained through a construction that generalizes the well-known model intersection theorem for classical logic programming. Finally, we show that by collapsing the true and false values of the infinite-valued model M P to (the classical) True and False, we obtain a three-valued model identical to the well-founded one. © 2005 ACM

An infinite-valued semantics for logic programs with negation

We give a purely model-theoretic (denotational) characterization of the semantics of logic programs with negation allowed in clause bodies. In our semantics (the first of its kind) the meaning of a program is, as in the classical case, the unique minimum model in a programindependent ordering. We use an expanded truth domain that has an uncountable linearly ordered set of truth values between False (the minimum element) and True (the maximum), with a Zero element in the middle. The truth values below Zero are ordered like the countable ordinals. The values above Zero have exactly the reverse order. Negation is interpreted as refiection about Zero followed by a step towards Zero; the only truth value that remains unaffected by negation is Zero. We show that every program has a unique minimum model MP, and that this model can be constructed with a TP iteration which proceeds through the countable ordinals. Furthermore, collapsing the true and false values of the infinite-valued model MP to (the classical) True and False, gives a three-valued model identical to the well-founded one. © 2002 Springer-Verlag

Strong equivalence of logic programs under the infinite-valued semantics

We consider the notion of strong equivalence [V. Lifschitz, D. Pearce, A. Valverde, Strongly equivalent logic programs, ACM Transactions on Computational Logic 2 (4) (2001) 526-541] of normal propositional logic programs under the infinite-valued semantics [P. Rondogiannis, W.W. Wadge, Minimum model semantics for logic programs with negation-as-failure, ACM Transactions on Computational Logic 6 (2) (2005) 441-467] (which is a purely model-theoretic semantics that is compatible with the well-founded one). We demonstrate that two such programs are strongly equivalent under the infinite-valued semantics if and only if they are logically equivalent in the corresponding infinite-valued logic. In particular, we show that strong equivalence of normal propositional logic programs is decidable, and more specifically coNP-complete. Our results have a direct implication for the well-founded semantics since, as we demonstrate, if two programs are strongly equivalent under the infinite-valued semantics, then they are also strongly equivalent under the well-founded semantics. © 2009 Elsevier B.V. All rights reserved

An infinite-game semantics for well-founded negation in logic programming

We present an infinite-game characterization of the well-founded semantics for function-free logic programs with negation. Our game is a simple generalization of the standard game for negation-less logic programs introduced by van Emden [M.H. van Emden, Quantitative deduction and its fixpoint theory, Journal of Logic Programming 3 (1) (1986) 37-53] in which two players, the Believer and the Doubter, compete by trying to prove (respectively disprove) a query. The standard game is equivalent to the minimum Herbrand model semantics of logic programming in the sense that a query succeeds in the minimum model semantics iff the Believer has a winning strategy for the game which begins with the Doubter doubting this query. The game for programs with negation that we propose follows the same rules as the standard one, except that the players swap roles every time the play "passes through" negation. We start our investigation by establishing the determinacy of the new game by using some classical tools from the theory of infinite-games. Our determinacy result immediately provides a novel and purely game-theoretic characterization of the semantics of negation in logic programming. We proceed to establish the connections of the game semantics to the existing semantic approaches for logic programming with negation. For this purpose, we first define a refined version of the game that uses degrees of winning and losing for the two players. We then demonstrate that this refined game corresponds exactly to the infinite-valued minimum model semantics of negation [P. Rondogiannis,W.W. Wadge, Minimum model semantics for logic programs with negation-as-failure, ACM Transactions on Computational Logic 6 (2) (2005) 441-467]. This immediately implies that the unrefined game is equivalent to the well-founded semantics (since the infinite-valued semantics is a refinement of the well-founded semantics). © 2007 Elsevier B.V. All rights reserved