Resource-driven Substructural Defeasible Logic

Linear Logic and Defeasible Logic have been adopted to formalise different features relevant to agents: consumption of resources, and reasoning with exceptions. We propose a framework to combine sub-structural features, corresponding to the consumption of resources, with defeasibility aspects, and we discuss the design choices for the framework

Applications of Linear Defeasible Logic: combining resource consumption and exceptions to energy management and business processes

Linear Logic and Defeasible Logic have been adopted to formalise different features of knowledge representation: consumption of resources, and non monotonic reasoning in particular to represent exceptions. Recently, a framework to combine sub-structural features, corresponding to the consumption of resources, with defeasibility aspects to handle potentially conflicting information, has been discussed in literature, by some of the authors. Two applications emerged that are very relevant: energy management and business process management. We illustrate a set of guide lines to determine how to apply linear defeasible logic to those contexts.Comment: In Proceedings DICE-FOPARA 2019, arXiv:1908.04478. arXiv admin note: substantial text overlap with arXiv:1809.0365

A One-Pass Tree-Shaped Tableau for Defeasible LTL

Defeasible Linear Temporal Logic is a defeasible temporal formalism for representing and verifying exception-tolerant systems. It is based on Linear Temporal Logic (LTL) and builds on the preferential approach of Kraus et al. for non-monotonic reasoning, which allows us to formalize and reason with exceptions. In this paper, we tackle the satisfiability checking problem for defeasible LTL. One of the methods for satisfiability checking in LTL is the one-pass tree shaped analytic tableau proposed by Reynolds. We adapt his tableau to defeasible LTL by integrating the preferential semantics to the method. The novelty of this work is in showing how the preferential semantics works in a tableau method for defeasible linear temporal logic. We introduce a sound and complete tableau method for a fragment that can serve as the basis for further exploring tableau methods for this logic

Operational semantics for signal handling

Signals are a lightweight form of interprocess communication in Unix. When a process receives a signal, the control flow is interrupted and a previously installed signal handler is run. Signal handling is reminiscent both of exception handling and concurrent interleaving of processes. In this paper, we investigate different approaches to formalizing signal handling in operational semantics, and compare them in a series of examples. We find the big-step style of operational semantics to be well suited to modelling signal handling. We integrate exception handling with our big-step semantics of signal handling, by adopting the exception convention as defined in the Definition of Standard ML. The semantics needs to capture the complex interactions between signal handling and exception handling.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244

Induction of Non-Monotonic Logic Programs to Explain Boosted Tree Models Using LIME

We present a heuristic based algorithm to induce \textit{nonmonotonic} logic programs that will explain the behavior of XGBoost trained classifiers. We use the technique based on the LIME approach to locally select the most important features contributing to the classification decision. Then, in order to explain the model's global behavior, we propose the LIME-FOLD algorithm ---a heuristic-based inductive logic programming (ILP) algorithm capable of learning non-monotonic logic programs---that we apply to a transformed dataset produced by LIME. Our proposed approach is agnostic to the choice of the ILP algorithm. Our experiments with UCI standard benchmarks suggest a significant improvement in terms of classification evaluation metrics. Meanwhile, the number of induced rules dramatically decreases compared to ALEPH, a state-of-the-art ILP system

An LTL Semantics of Business Workflows with Recovery

We describe a business workflow case study with abnormal behavior management (i.e. recovery) and demonstrate how temporal logics and model checking can provide a methodology to iteratively revise the design and obtain a correct-by construction system. To do so we define a formal semantics by giving a compilation of generic workflow patterns into LTL and we use the bound model checker Zot to prove specific properties and requirements validity. The working assumption is that such a lightweight approach would easily fit into processes that are already in place without the need for a radical change of procedures, tools and people's attitudes. The complexity of formalisms and invasiveness of methods have been demonstrated to be one of the major drawback and obstacle for deployment of formal engineering techniques into mundane projects

Graphs Identified by Logics with Counting

We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a structure is identified by C2. Our classification implies that for every graph identified by this logic, all vertex-colored versions of it are also identified. A similar statement is true for finite relational structures. We provide constructions that solve the inversion problem for finite structures in linear time. This problem has previously been shown to be polynomial time solvable by Martin Otto. For graphs, we conclude that every C2-equivalence class contains a graph whose orbits are exactly the classes of the C2-partition of its vertex set and which has a single automorphism witnessing this fact. For general k, we show that such statements are not true by providing examples of graphs of size linear in k which are identified by C3 but for which the orbit partition is strictly finer than the Ck-partition. We also provide identified graphs which have vertex-colored versions that are not identified by Ck.Comment: 33 pages, 8 Figure