Logic & Formal Reasoning
Artificial intelligence plus common sense
In the future, a new generation of autonomous robots is set to complete tasks autonomously, even if something unforeseeable happens. With the support of the Austrian Science Fund FWF, information technology experts in Graz are working to advance the development of artificial intelligence and equip robots with common sense. Something that children learn through play and that adults are able to do on the basis of past experience, such as responding to unexpected situations, remains one of the great challenges in robotics. Autonomous systems are expected to complete tasks given to them without external input. The deployment of such intelligent robots would be particularly important in critical situations – such as environmental disasters or industrial accidents.
Probabilistic Theorem Proving
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logical structure into account. We propose the first method that has the full power of both graphical model inference and first-order theorem proving (in finite domains with Herbrand interpretations). We first define probabilistic theorem proving (PTP), their generalization, as the problem of computing the probability of a logical formula given the probabilities or weights of a set of formulas.
Technical Perspective: Combining Logic and Probability
A goal of research in artificial intelligence and machine learning since the early days of expert systems has been to develop automated reasoning methods that combine logic and probability. Why is there a need to combine logic and probability? Probability theory allows one to quantify uncertainty over a set of propositions--ground facts about the world--and a probabilistic reasoning system allows one to infer the probability of unknown (hidden) propositions conditioned on the knowledge of other propositions. However, probability theory alone has nothing to say about how propositions are constructed from relationships over entities or tuples of entities, and how general knowledge at the level of relationships is to be represented and applied.
Two Aspects of Relevance in Structured Argumentation: Minimality and Paraconsistency
Grooters, Diana, Prakken, Henry
This paper studies two issues concerning relevance in structured argumentation in the context of the ASPIC+ framework, arising from the combined use of strict and defeasible inference rules. One issue arises if the strict inference rules correspond to classical logic. A longstanding problem is how the trivialising effect of the classical Ex Falso principle can be avoided while satisfying consistency and closure postulates. In this paper, this problem is solved by disallowing chaining of strict rules, resulting in a variant of the ASPIC+ framework called ASPIC*, and then disallowing the application of strict rules to inconsistent sets of formulas. Thus in effect Rescher & Manor's paraconsistent notion of weak consequence is embedded in ASPIC*. Another issue is minimality of arguments. If arguments can apply defeasible inference rules, then they cannot be required to have subset-minimal premises, since defeasible rules based on more information may well make an argument stronger. In this paper instead minimality is required of applications of strict rules throughout an argument. It is shown that under some plausible assumptions this does not affect the set of conclusions. In addition, circular arguments are in the new ASPIC* framework excluded in a way that satisfies closure and consistency postulates and that generates finitary argumentation frameworks if the knowledge base and set of defeasible rules are finite. For the latter result the exclusion of chaining of strict rules is essential. Finally, the combined results of this paper are shown to be a proper extension of classical-logic argumentation with preferences and defeasible rules.
History of artificial intelligence - Wikipedia, the free encyclopedia
The history of artificial intelligence (AI) began in antiquity, with myths, stories and rumors of artificial beings endowed with intelligence or consciousness by master craftsmen; as Pamela McCorduck writes, AI began with "an ancient wish to forge the gods."[1] The seeds of modern AI were planted by classical philosophers who attempted to describe the process of human thinking as the mechanical manipulation of symbols. This work culminated in the invention of the programmable digital computer in the 1940s, a machine based on the abstract essence of mathematical reasoning. This device and the ideas behind it inspired a handful of scientists to begin seriously discussing the possibility of building an electronic brain. The Turing test was proposed by British mathematician Alan Turing in his 1950 paper Computing Machinery and Intelligence, which opens with the words: "I propose to consider the question, 'Can machines think?'" The term'Artificial Intelligence' was created at a conference held at Dartmouth College in 1956.[2] Allen Newell, J. C. Shaw, and Herbert A. Simon pioneered the newly created artificial intelligence field with the Logic Theory Machine (1956), and the General Problem Solver in 1957.[3] In 1958, John McCarthy and Marvin Minsky started the MIT Artificial Intelligence lab with 50,000.[4] John McCarthy also created LISP in the summer of 1958, a programming language still important in artificial intelligence research.[5] In 1973, in response to the criticism of James Lighthill and ongoing pressure from congress, the U.S. and British Governments stopped funding undirected research into artificial intelligence. Seven years later, a visionary initiative by the Japanese Government inspired governments and industry to provide AI with billions of dollars, but by the late 80s the investors became disillusioned and withdrew funding again. McCorduck (2004) writes "artificial intelligence in one form or another is an idea that has pervaded Western intellectual history, a dream in urgent need of being realized," expressed in humanity's myths, legends, stories, speculation and clockwork automatons.[6] Mechanical men and artificial beings appear in Greek myths, such as the golden robots of Hephaestus and Pygmalion's Galatea.[7] In the Middle Ages, there were rumors of secret mystical or alchemical means of placing mind into matter, such as J?bir ibn Hayy?n's Takwin, Paracelsus' homunculus and Rabbi Judah Loew's Golem.[8] By the 19th century, ideas about artificial men and thinking machines were developed in fiction, as in Mary Shelley's Frankenstein or Karel?apek's
Learning Relational Dynamics of Stochastic Domains for Planning
Martínez, David (Institut de Robòtica i Informàtica Industrial (CSIC-UPC)) | Alenyà, Guillem (Institut de Robòtica i Informàtica Industrial (CSIC-UPC)) | Torras, Carme (Institut de Robòtica i Informàtica Industrial (CSIC-UPC)) | Ribeiro, Tony (IRCCyN, École Centrale de Nantes) | Inoue, Katsumi (National Institute of Informatics, Japan)
Probabilistic planners are very flexible tools that can provide good solutions for difficult tasks. However, they rely on a model of the domain, which may be costly to either hand code or automatically learn for complex tasks. We propose a new learning approach that (a) requires only a set of state transitions to learn the model; (b) can cope with uncertainty in the effects; (c) uses a relational representation to generalize over different objects; and (d) in addition to action effects, it can also learn exogenous effects that are not related to any action, e.g., moving objects, endogenous growth and natural development. The proposed learning approach combines a multi-valued variant of inductive logic programming for the generation of candidate models, with an optimization method to select the best set of planning operators to model a problem. Finally, experimental validation is provided that shows improvements over previous work.
Assessing the Expressivity of Planning Formalisms through the Comparison to Formal Languages
Höller, Daniel (Ulm University) | Behnke, Gregor (Ulm University) | Bercher, Pascal (Ulm University) | Biundo, Susanne (Ulm University)
From a theoretical perspective, judging the expressivity of planning formalisms helps to understand the relationship of different representations and to infer theoretical properties. From a practical point of view, it is important to be able to choose the best formalism for a problem at hand, or to ponder the consequences of introducing new representation features. Most work on the expressivity is based either on compilation approaches, or on the computational complexity of the plan existence problem. Recently, we introduced a new notion of expressivity. It is based on comparing the structural complexity of the set of solutions to a planning problem by interpreting the set as a formal language and classifying it with respect to the Chomsky hierarchy. This is a more direct measure than the plan existence problem and enables also the comparison of formalisms that can not be compiled into each other. While existing work on that last approach focused on different hierarchical problem classes, this paper investigates STRIPS with and without conditional effects; though we also tighten some existing results on hierarchical formalisms. Our second contribution is a discussion on the language-based expressivity measure with respect to the other approaches.
A Theory of Formal Synthesis via Inductive Learning
Jha, Susmit, Seshia, Sanjit A.
Formal synthesis is the process of generating a program satisfying a high-level formal specification. In recent times, effective formal synthesis methods have been proposed based on the use of inductive learning. We refer to this class of methods that learn programs from examples as formal inductive synthesis. In this paper, we present a theoretical framework for formal inductive synthesis. We discuss how formal inductive synthesis differs from traditional machine learning. We then describe oracle-guided inductive synthesis (OGIS), a framework that captures a family of synthesizers that operate by iteratively querying an oracle. An instance of OGIS that has had much practical impact is counterexample-guided inductive synthesis (CEGIS). We present a theoretical characterization of CEGIS for learning any program that computes a recursive language. In particular, we analyze the relative power of CEGIS variants where the types of counterexamples generated by the oracle varies. We also consider the impact of bounded versus unbounded memory available to the learning algorithm. In the special case where the universe of candidate programs is finite, we relate the speed of convergence to the notion of teaching dimension studied in machine learning theory. Altogether, the results of the paper take a first step towards a theoretical foundation for the emerging field of formal inductive synthesis.