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 Logic & Formal Reasoning


A Natural Language Question Answering System as a Participant in Human Q&A Portals

AAAI Conferences

LogAnswer is a question answering (QA) system for the German language, aimed at providing concise and correct answers to arbitrary questions. For this purpose LogAnswer is designed as an embedded artificial intelligence system which integrates methods from several fields of AI, namely natural language processing, machine learning, knowledge representation and automated theorem proving. We intend to employ LogAnswer as a virtual user within Internet-based QA forums, where it must be able to identify the questions that it cannot answer correctly, a task that normally receives little attention in QA research compared to the actual answer derivation. The paper presents a machine learning solution to the wrong answer avoidance (WAA) problem, applying a meta classifier to the output of simple term-based classifiers and a rich set of other WAA features. Experiments with a large set of real-world questions from a QA forum show that the proposed method significantly improves the WAA characteristics of our system.


Learning for Deep Language Understanding

AAAI Conferences

Lexicalized Well-Founded Grammar (LWFG) is a recently developed syntactic-semantic grammar formalism for deep language understanding, which balances expressiveness with provable learnability results. The learnability result for LWFGs assumes that the semantic composition constraints are learnable. In this paper, we show what are the properties and principles the semantic representation and grammar formalism require, in order to be able to learn these constraints from examples, and give a learning algorithm. We also introduce a LWFG parser as a deductive system, used as an inference engine during LWFG induction. An example for learning a grammar for noun compounds is given.


Learning from Natural Instructions

AAAI Conferences

Machine learning is traditionally formalized and researched as the study of learning concepts and decision functions from labeled examples, requiring a representation that encodes information about the domain of the decision function to be learned. We are interested in providing a way for a human teacher to interact with an automated learner using natural instructions, thus allowing the teacher to communicate the relevant domain expertise to the learner without necessarily knowing anything about the internal representations used in the learning process. In this paper we suggest to view the process of learning a decision function as a natural language lesson interpretation problem instead of learning from labeled examples. This interpretation of machine learning is motivated by human learning processes, in which the learner is given a lesson describing the target concept directly, and a few instances exemplifying it. We introduce a learning algorithm for the lesson interpretation problem that gets feedback from its performance on the final task, while learning jointly (1) how to interpret the lesson and (2) how to use this interpretation to do well on the final task. his approach alleviates the supervision burden of traditional machine learning by focusing on supplying the learner with only human-level task expertise for learning. We evaluate our approach by applying it to the rules of the Freecell solitaire card game. We show that our learning approach can eventually use natural language instructions to learn the target concept and play the game legally. Furthermore, we show that the learned semantic interpreter also generalizes to previously unseen instructions.


Translating First-Order Theories into Logic Programs

AAAI Conferences

This paper focuses on computing first-order theories under either stable model semantics or circumscription. A reduction from first-order theories to logic programs under stable model semantics over finite structures is proposed, and an embedding of circumscription into stable model semantics is also given. Having such reduction and embedding, reasoning problems represented by first-order theories under these two semantics can then be handled by using existing answer set solvers. The effectiveness of this approach in computing hard problems beyond NP is demonstrated by some experiments.


Consequence-Based Reasoning beyond Horn Ontologies

AAAI Conferences

Consequence-based ontology reasoning procedures have so far been known only for Horn ontology languages. A difficulty in extending such procedures is that non-Horn axioms seem to require reasoning by case, which causes non-determinism in tableau-based procedures. In this paper we present a consequence-based procedure for ALCH that overcomes this difficulty by using rules similar to ordered resolution to deal with disjunctive axioms in a deterministic way; it retains all the favourable attributes of existing consequence-based procedures, such as goal-directed โ€œone passโ€ classification, optimal worst-case complexity, and โ€œpay-asyou- goโ€ behaviour. Our preliminary empirical evaluation suggests that the procedure scales well to non-Horn ontologies.


Description Logics and Fuzzy Probability

AAAI Conferences

Uncertainty and vagueness are pervasive phenomena in real-life knowledge. They are supported in extended description logics that adapt classical description logics to deal with numerical probabilities or fuzzy truth degrees. While the two concepts are distinguished for good reasons, they combine in the notion of probably, which is ultimately a fuzzy qualification of probabilities. Here, we develop existing propositional logics of fuzzy probability into a full-blown description logic, and we show decidability of several variants of this logic under Lukasiewicz semantics. We obtain these results in a novel generic framework of fuzzy coalgebraic logic; this enables us to extend our results to logics that combine crisp ingredients including standard crisp roles and crisp numerical probabilities with fuzzy roles and fuzzy probabilities.


A Logical Formulation for Negotiation Among Dishonest Agents

AAAI Conferences

The paper introduces a logical framework for negotiation among dishonest agents. The framework relies on the use of abductive logic programming as a knowledge representation language for agents to deal with incomplete information and preferences. The paper shows how intentionally false or inaccurate information of agents could be encoded in the agents' knowledge bases. Such disinformation can be effectively used in the process of negotiation to have desired outcomes by agents. The negotiation processes are formulated under the answer set semantics of abductive logic programming and enable the exploration of various strategies that agents can employ in their negotiation


Dishonest Reasoning by Abduction

AAAI Conferences

This paper studies a computational logic for dishonest reasoning. We introduce logic programs with disinformation to represent and reason with dishonesty. We then consider two different cases of dishonesty: deductive dishonesty and abductive dishonesty. The former misleads another agent to deduce wrong conclusions, while the latter interrupts another agent to abduce correct explanations. In deductive or abductive dishonesty, an agent can perform different types of dishonest reasoning such as lying, bullshitting, and withholding information. We show that these different types of dishonest reasoning are characterized by extended abduction, and address their computational methods using abductive logic programming.


An Approach to Minimal Belief Via Objective Belief

AAAI Conferences

As a doxastic counterpart to epistemic logic based on S5 we study the modal logic KSD that can be viewed as an approach to modelling a kind of objective and fair belief. We apply KSD to the problem of minimal belief and develop an alterna- tive approach to nonmonotonic modal logic using a weaker concept of expansion. This corresponds to a certain minimal kind of KSD model and yields a new type of nonmonotonic doxastic reasonin


Revisiting Preferences and Argumentation

AAAI Conferences

The ASPIC+ framework is intermediate in abstraction between Dung's argumentation framework and concrete instantiating logics. This paper generalises ASPIC+ to accommodate classical logic instantiations, and adopts a new proposal for evaluating extensions: attacks are used to define the notion of conflict-free sets, while the defeats obtained by applying preferences to attacks, are exclusively used to determine the acceptability of arguments. Key properties and rationality postulates are then shown to hold for the new framework.