The canonical linguistic process is the cycle of the speech-circuit [Saussure, 1915]. A speaker expresses a psychological idea by means of a physiological articulation. The signal is transmitted through the medium by a physical process incident on a hearer who from the consequent physiological impression recovers the psychological idea. The hearer may then reply, swapping the roles of speaker and hearer, and so the circuit cycles. For communication to be successful speakers and hearers must have shared associations between forms (signifiers) andmeanings(signifieds). De Saussure called such a pairing of signifier and signified a sign. Therelationisone-to-many (ambiguity) and many-to-one (paraphrase). Let us call a stable totality of such associations a language. It would be arbitrary to propose that there is a longest expression (where would we propose to cut off IknowthatyouknowthatIknow that you know...?) therefore language is an infinite abstraction over the finite number of acts of communication that can ever occur. The program of formal syntax [Chomsky, 1957] is to define the set of all and only

What is an inference rule? This question does not have a unique answer. One usually nds two distinct standard answers in the literature: validity inference ( ` v ' if for every substitution , the validity of [] entails the validity of [']), and truth inference ( ` t ' if for every substitution , the truth of [] entails the truth of [']). In this paper we introduce a general semantic framework that allows us to investigate the notion of inference more carefully. Validity inference and truth inference are in some sense the extremal points in our framework. We investigate the relationship between various types of inference in our general framework, and consider the complexity of deciding if an inference rule is sound, in the context of a number of logics of interest: classical propositional logic, a nonstandard propositional logic, various propositional modal logics, and rst-order logic.

In Linked Data, the use of owl:sameAs is ubiquitous in ‘inter-linking ’ data-sets. However, there is a lurking suspicion within the Linked Data community that this use of owl:sameAs may be somehow incorrect, in particular with regards to its interactions with inference. In fact, owl:sameAs can be considered just one type of ‘identity link, ’ a link that declares two items to be identical in some fashion. After reviewing the definitions and history of the problem of identity in philosophy and knowledge representation, we outline four alternative readings of owl:sameAs, showing with examples how it is being (ab)used on the Web of data. Then we present possible solutions to this problem by introducing alternative identity links that rely on named graphs.

Abstract 2 Most autonomous agents are situated in a social context and need to interact with other agents (both human and artificial) to complete their problem solving objectives. Such agents are usually capable of performing a wide range of actions and engaging in a variety of social interactions. Faced with this variety of options, an agent must decide what to do. There are many potential decision making functions that could be employed to make the choice. Each such function will have a different effect on the success of the individual agent and of the overall system in which it is situated. To this end, this thesis examines agents ’ decision making functions to ascertain their likely properties and attributes. A novel framework for characterising social decision making is presented which provides explicit reasoning about the potential benefits of the individual agent, particular sub-groups of agents or the overall system. This framework enables multi-farious social interaction attitudes to be identified and defined; ranging from the purely self-interested to the purely altruistic. In particular, however, the focus is on the spectrum of socially responsible agent behaviours in which agents attempt to balance their own needs with those of the overall system. Such behaviour aims to ensure that both the agent and the overall system perform well.

This thesis analyzes the connections between resolution proofs and satisfiability search procedures. It is well known that DLL search algorithms that do not use learning are equivalent to tree-like resolution in terms of proof complexity. To generalize this result to DLL algorithms that use learning, two natural generalizations of regular resolution that are based on resolution trees with lemmas (RTL) are introduced. It is shown that dag-like resolution is equivalent to these resolution refinements when there is no regularity condition. On the other hand an exponential separation between the regular versions (regular weak resolution trees with input lemmas and regular weak resolution trees with lemmas) and regular dag-like resolution is given. It is proved that executions of DLL algorithms that use learning based on the conflict graph and unit propagation, like most of the current state of the art SAT-solvers, can be simulated by regular WRTL. Inspired by this simulation, a new generalization of learning in DLL algorithms, which is polynomially equivalent to regular WRTL, is presented. This algorithm can simulate general

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Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspective of knowledge representation, their formal languages were not sufficiently expressive. On the other hand, most logicians were not concerned about the possibility of automated reasoning; from the perspective of knowledge representation, they were often too generous in the choice of syntactic constructs. In spite of these differences, classical mathematical logic has exerted significant influence on knowledge representation research, and it is appropriate to begin this handbook with a discussion of the relationship between these fields. The language of classical logic that is most widely used in the theory of knowledge representation is the language of first-order (predicate) formulas. These are the formulas that John McCarthy proposed to use for representing declarative knowledge in his advice taker paper [176], and Alan Robinson proposed to prove automatically using resolution [236]. Propositional logic is, of course, the most important subset of first-order logic; recent

Both in Kripke's Theory of Truth ktt [8] and Russell's Ramified Type Theory rtt [16, 9] we are confronted with some hierarchy. In rtt, we have a double hierarchy of orders and types. That is, the class of propositions is divided into different orders where a propositional function can only depend on objects of lower orders and types. Kripke on the other hand, has a ladder of languages where the truth of a proposition in language Ln can only be made in Lm where m ? n. Kripke finds a fixed point for his hierarchy (something Russell does not attempt to do). We investigate in this paper the similarities of both hierarchies: At level n of ktt the truth or falsehood of all order-n-propositions of rtt can be established. Moreover, there are order-n-propositions that get a truth value at an earlier stage in ktt. Furthermore, we show that rtt is more restrictive than ktt, as some type restrictions are not needed in ktt and more formulas can be expressed in the latter. Looking back at the dou...

Traditionally logic was considered as having two branches: deductive and inductive. However the development of the subject from Frege (1879) up to about 1970 brought about a divergence between deductive and inductive logic. It is argued in this paper that developments in artificial intelligence in the last twenty or so years (particularly logic programming and machine learning) have created a new framework for logic in which deductive and inductive logic can, once again, be treated as similar branches of the same discipline. Keywords: deductive logic, inductive logic, logic programming, machine learning, PROLOG 1 Introduction The aim of this paper is to explore some consequences for the philosophy of logic and the philosophy of science of advances in artificial intelligence (AI) made in the last twenty or so years. Let me begin by listing some of these advances. I will describe the philosophically relevant aspects of these developments in more detail later. As far as the philosophy o...