Logic & Formal Reasoning
Readings in Medical Artificial Intelligence
JANICE S. AIKINS Dr. Aikins received her Ph.D. in computer science from Stanford University in 1980. She is currently a research computer scientist at IBM's Palo Alto Scientific Center. She specializes in designing systems with an emphasis on the explicit representation of control knowledge in expert systems. ROBERT L. BLUM Dr. Blum received his M.D. from the University of California Medical School at San Francisco in 1973. From 1973 to 1976 he did an internship and residency in the Department of Internal Medicine at the Kaiser Foundation Hospital in Oakland, California, where he was chief resident in 1976.
It could be worse, it could be raining: reliable automatic meteorological forecasting
Cristani, Matteo, Domenichini, Francesco, Tomazzoli, Claudio, Viganรฒ, Luca, Zorzi, Margherita
Meteorological forecasting provides reliable prediction about the future weather within a given interval of time. Meteorological forecasting can be viewed as a form of hybrid diagnostic reasoning and can be mapped onto an integrated conceptual framework. The automation of the forecasting process would be helpful in a number of contexts, in particular: when the amount of data is too wide to be dealt with manually; to support forecasters education; when forecasting about underpopulated geographic areas is not interesting for everyday life (and then is out from human forecasters' tasks) but is central for tourism sponsorship. We present logic MeteoLOG, a framework that models the main steps of the reasoner the forecaster adopts to provide a bulletin. MeteoLOG rests on several traditions, mainly on fuzzy, temporal and probabilistic logics. On this basis, we also introduce the algorithm Tournament, that transforms a set of MeteoLOG rules into a defeasible theory, that can be implemented into an automatic reasoner. We finally propose an example that models a real world forecasting scenario.
Learning Ontologies with Epistemic Reasoning: The EL Case
We investigate the problem of learning description logic ontologies from entailments via queries, using epistemic reasoning. We introduce a new learning model consisting of epistemic membership and example queries and show that polynomial learnability in this model coincides with polynomial learnability in Angluin's exact learning model with membership and equivalence queries. We then instantiate our learning framework to EL and show some complexity results for an epistemic extension of EL where epistemic operators can be applied over the axioms. Finally, we transfer known results for EL ontologies and its fragments to our learning model based on epistemic reasoning.
Relative Entailment Among Probabilistic Implications
Atserias, Albert, Balcรกzar, Josรฉ L., Piceno, Marie Ely
We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is defined in terms of a threshold on a conditional probability of the consequent, given the antecedent: we are dealing with what the data analysis community calls confidence of partial implications or association rules. Existing studies of redundancy among these partial implications have characterized so far only entailment from one premise and entailment from two premises, both in the stand-alone case and in the case of presence of additional classical implications (this is what we call "relative entailment"). By exploiting a previously noted alternative view of the entailment in terms of linear programming duality, we characterize exactly the cases of entailment from arbitrary numbers of premises, again both in the stand-alone case and in the case of presence of additional classical implications. As a result, we obtain decision algorithms of better complexity; additionally, for each potential case of entailment, we identify a critical confidence threshold and show that it is, actually, intrinsic to each set of premises and antecedent of the conclusion.
Active Automata Learning with Adaptive Distinguishing Sequences
The ever-growing complexity of today's soft-and hardware makes testing both an indispensable necessityand a challenging task. At the given scale, manual testing is unfeasible, which raises the urge for automated approaches. At the same time, the ongoing digitalization ofsecurity-and safety-centric applications requires exhaustive verification of key properties. A field of research that tackles these problems and has yielded sophisticating results is that of model-based testing [Bro 05] and model checking [BK08]. Formal verification methods, depending on the scenario, allow the automated generation of tests or the automated evaluation of test properties. Being based on formal models, a successful verification is also able to provably guarantee certain properties of the system under testing. Key to a successful application of these techniques is a formal specification of the target system. This requirement, however, poses a problem to many real-world applications: Thelack of formal specifications for software or hardware hinders the employment of formal verification methods. Creating formal specifications for soft-or hardware components is not only a tedious task but also prone to errors.
Increasing city safety awareness regarding disruptive traffic stream
Transportation systems serve the people in essence, in this study we focus in traffic information related to violation events to respond to safety requirements of the cities. Traffic violation events have an important role in city safety awareness and secure travel. In this work, we describe the use of knowledge discovery from traffic violation reports in combination with demographics approach using inductive logic programming to automatically extract knowledge about traffic violation behavior and their impact on the environment.
A Generalisation of AGM Contraction and Revision to Fragments of First-Order Logic
Zhuang, Zhiqiang, Wang, Zhe, Wang, Kewen, Delgrande, James
AGM contraction and revision assume an underlying logic that contains propositional logic. Consequently, this assumption excludes many useful logics such as the Horn fragment of propositional logic and most description logics. Our goal in this paper is to generalise AGM contraction and revision to (near-)arbitrary fragments of classical first-order logic. To this end, we first define a very general logic that captures these fragments. In so doing, we make the modest assumptions that a logic contains conjunction and that information is expressed by closed formulas or sentences. The resulting logic is called first-order conjunctive logic or FC logic for short. We then take as the point of departure the AGM approach of constructing contraction functions through epistemic entrenchment, that is the entrenchment-based contraction. We redefine entrenchment-based contraction in ways that apply to any FC logic, which we call FC contraction. We prove a representation theorem showing its compliance with all the AGM contraction postulates except for the controversial recovery postulate. We also give methods for constructing revision functions through epistemic entrenchment which we call FC revision; which also apply to any FC logic. We show that if the underlying FC logic contains tautologies then FC revision complies with all the AGM revision postulates. Finally, in the context of FC logic, we provide three methods for generating revision functions via a variant of the Levi Identity, which we call contraction, withdrawal and cut generated revision, and explore the notion of revision equivalence. We show that withdrawal and cut generated revision coincide with FC revision and so does contraction generated revision under a finiteness condition.
Knowledge Refinement via Rule Selection
Kolaitis, Phokion G., Popa, Lucian, Qian, Kun
In several different applications, including data transformation and entity resolution, rules are used to capture aspects of knowledge about the application at hand. Often, a large set of such rules is generated automatically or semi-automatically, and the challenge is to refine the encapsulated knowledge by selecting a subset of rules based on the expected operational behavior of the rules on available data. In this paper, we carry out a systematic complexity-theoretic investigation of the following rule selection problem: given a set of rules specified by Horn formulas, and a pair of an input database and an output database, find a subset of the rules that minimizes the total error, that is, the number of false positive and false negative errors arising from the selected rules. We first establish computational hardness results for the decision problems underlying this minimization problem, as well as upper and lower bounds for its approximability. We then investigate a bi-objective optimization version of the rule selection problem in which both the total error and the size of the selected rules are taken into account. We show that testing for membership in the Pareto front of this bi-objective optimization problem is DP-complete. Finally, we show that a similar DP-completeness result holds for a bi-level optimization version of the rule selection problem, where one minimizes first the total error and then the size.
Strong Equivalence and Program's Structure in Arguing Essential Equivalence between Logic Programs
Answer set programming is a prominent declarative programming paradigm used in formulating combinatorial search problems and implementing distinct knowledge representation formalisms. It is common that several related and yet substantially different answer set programs exist for a given problem. Sometimes these encodings may display significantly different performance. Uncovering {\em precise formal} links between these programs is often important and yet far from trivial. This paper claims the correctness of a number of interesting program rewritings.