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 Logic & Formal Reasoning


Domain Modeling for Planning as Logic Programming

AAAI Conferences

Planning as programming is an approach to automated planning, where the planning domain model is expressed as a program in some (declarative) programming language. Then the modeler can exploit all features of that language to encode control knowledge important for efficient planning. In this paper we study these features in the logic programming language Picat and its planner module. In particular, we use two planning benchmarks, Nomystery and Childsnack, to compare factored and structured representations of states extended by encodings of control knowledge.


12 Best Free Ebooks for Machine Learning

#artificialintelligence

Machine learning is a scientific discipline that works on construction and study of algorithms which operate by building a model from example inputs using the make predictions or decisions. With the number of people joining the nerdy geeks, machine learning has seen quite a lot of development over the course of years. Are you the one who has recently started or is planning to start the career in machine learning? If your answer is yes, I won't scare you with the words like it's quite a difficult job but then its hard nut to crack and if you take it as a motivation you will understand what I am trying to say. Many things in this world are difficult or they appear to be in the beginning but are not impossible.


Parameterized Complexity Results for Symbolic Model Checking of Temporal Logics

AAAI Conferences

Reasoning about temporal knowledge is a fundamental task in the area of artificial intelligence and knowledge representation. A key problem in this area is model checking, and indispensable for the state-of-the-art in solving this problem in large-scale settings is the technique of bounded model checking. We investigate the theoretical possibilities of this technique using parameterized complexity theory. In particular, we provide a complete parameterized complexity classification for the model checking problem for symbolically represented Kripke structures for various fragments of the temporal logics LTL, CTL and CTL*. We argue that a known result from the literature for a restricted fragment of LTL can be seen as an fpt-reduction to SAT, and show that such reductions are not possible for any of the other fragments of the temporal logics that we consider. As a by-product of our investigation, we develop a novel parameterized complexity class that can be seen as a parameterized variant of the Polynomial Hierarchy.


Reasoning about Truthfulness of Agents Using Answer Set Programming

AAAI Conferences

We propose a declarative framework for representing and reasoning about truthfulness of agents using answer set programming. We show how statements by agents can be evaluated against a set of observations over time equipped with our knowledge about the actions of the agents and the normal behavior of agents. We illustrate the framework using examples and discuss possible extensions that need to be considered.


Minimality Postulates for Ontology Revision

AAAI Conferences

In many scenarios where the integration of information into a knowledge base (KB) leads to inconsistencies there is a need to change the KB minimally. In belief revision, relevance postulates meet the minimality requirement by restricting the elimination of KB elements to those that are relevant for the incoming information. This paper focuses on two minimality postulates in an ontology revision scenario in which conflicts are caused by ambiguous use of symbols: a relevance postulate and a generalized inclusion postulate which limits the creativity of the operators. Both postulates exploit the (satisfiably) equivalent representation of a first-order logic KB by its prime implicates, which, intuitively, represent the most atomic logical components of the KB. The paper shows that reinterpretation operators (which are ontology revision operators) fulfill both postulates.


Infinite Paths in the Situation Calculus: Axiomatization and Properties

AAAI Conferences

The situation calculus has proved to be a very popular formalism for modeling and reasoning about dynamic systems. This otherwise elegant and refined language however lacks a natural way of dealing with "infinite future histories". To this end, in this paper we introduce a new sort ranging over infinite paths in the situation calculus and propose an axiomatization for infinite paths. We thus obtain a convenient way of specifying several kinds of notions that involve infinite futures such as temporal properties of non-terminating executions of agents or programs and mental attitudes such as desires and intentions. We prove the correctness of the axiomatization and show that our formalization has some intuitively desirable properties.



Negation Without Negation in Probabilistic Logic Programming

AAAI Conferences

Probabilistic logic programs without negation can have cycles (with a preference for false), but cannot represent all conditional distributions. Probabilistic logic programs with negation can represent arbitrary conditional probabilities, but with cycles they create logical inconsistencies. We show how allowing negative noise probabilities allows us to represent arbitrary conditional probabilities without negations. Noise probabilities for non-exclusive rules are difficult to interpret and unintuitive to manipulate; to alleviate this we define ``probability-strengths'' which provide an intuitive additive algebra for combining rules. For acyclic programs we prove what constraints on the strengths allow for proper distributions on the non-noise variables and allow for all non-extreme distributions to be represented. We show how arbitrary CPDs can be converted into this form in a canonical way. Furthermore, if a joint distribution can be compactly represented by a cyclic program with negations, we show how it can also be compactly represented with negative noise probabilities and no negations. This allows algorithms for exact inference that do not support negations to be applicable to probabilistic logic programs with negations.


An Abstract Logical Approach to Characterizing Strong Equivalence in Logic-based Knowledge Representation Formalisms

AAAI Conferences

We consider knowledge representation (KR) formalisms as collections of finite knowledge bases with a model-theoretic semantics. In this setting, we show that for every KR formalism there is a formalism that characterizes strong equivalence in the original formalism, that is unique up to isomorphism and that has a model theory similar to classical logic.


Online Situation-Determined Agents and their Supervision

AAAI Conferences

Agent supervision is a form of control/customization where a supervisor restricts the behavior of an agent to enforce certain requirements, while leaving the agent as much autonomy as possible. In this work, we investigate supervision of an agent that may acquire new knowledge about her environment during execution, for example, by sensing. Thus we consider an agent's online executions, where, as she executes the program, at each time point she must make decisions on what to do next based on what her current knowledge is. This is done in a setting based on the situation calculus and a variant of the ConGolog programming language. To reason about such agents, we first define a notion of online situation-determined agent which ensures that for any sequence of actions that the agent can perform online, the resulting agent configuration is unique. We then present our formalization of the online maximally permissive supervisor.