This paper describes a compositional shape analysis, where each procedure is analyzed independently of its callers. The analysis uses an abstract domain based on a restricted fragment of separation logic, and assigns a collection of Hoare triples to each procedure; the triples provide an over-approximation of data structure usage. Compositionality brings its usual benefits – increased potential to scale, ability to deal with unknown calling contexts, graceful way to deal with imprecision – to shape analysis, for the first time. The analysis rests on a generalized form of abduction (inference of explanatory hypotheses) which we call bi-abduction. Biabduction displays abduction as a kind of inverse to the frame problem: it jointly infers anti-frames (missing portions of state) and frames (portions of state not touched by an operation), and is the basis of a new interprocedural analysis algorithm. We have implemented

Formal AI systems traditionally represent knowledge using logical formulas.

Non-Axiomatic Reasoning System is an adaptive system that works with insu cient knowledge and resources. At the beginning of the paper, three binary term logics are de ned. The rst is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intension, and they also have interesting relations with Aristotle's syllogistic logic. Based on the three simple systems, a Non-Axiomatic Logic is de ned. It has a term-oriented language and an experience-grounded semantics. It can uniformly represents and processes randomness, fuzziness, and ignorance. It can also uniformly carries out deduction, abduction, induction, and revision.

Formal AI systems traditionally represent knowledge using logical formulas. Sometimes, however, a model-based representation is more compact and enables faster reasoning than the corresponding formula-based representation. The central idea behind our work is to represent a large set of models by a subset of characteristic models. More specifically, we examine model-based representations of Horn theories, and show that there are large Horn theories that can be exactly represented by an exponentially smaller set of characteristic models. We show that deduction based on a set of characteristic models requires only polynomial time, as it does using Horn theories. More surprisingly, abduction can be performed in polynomial time using a set of characteristic models, whereas abduction using Horn theories is NP-complete. Finally, we discuss algorithms for generating efficient representations of the Horn theory that best approximates a general set of models. 1 Introduction Logical formulas are...

Machine Due to the current technology of the computers we can use, we have chosen an extremely abridged emulation of the machine that will effectively run the programs, instead of more proper languages, like l-calculus (or LISP). We have adapted the "toy RISC" machine of [Hernndez & Hernndez 1993] with two remarkable features inherited from its object-oriented coding in C++: it is easily tunable for our needs, and it is efficient. We have made it even more reduced, removing any operand in the instruction set, even for the loop operations. We have only three registers which are AX (the accumulator), BX and CX. The operations Q b we have used for our experiment are in Table 1: LOOPTOP Decrements CX. If it is not equal to the first element jump to the program top.

ositive side, though, the second person might have some advantage over the first person in learning how to shift gears, because the second person would not have to overcome negative transfer from experience with automatic transmissions. As another example, imagine that you are an explorer visiting a remote island, with the purpose of writing a book about the people that you see there. You bring to this island many forms of prior knowledge that will guide you in learning about these new people. For example, based on your experiences in other places, you would expect to see males and females, younger and older people, shy people and arrogant people. You would also have certain hypotheses at a more abstract level, for example, that the clothes that someone wears may be related to the person's age and gender. (Goodman, 1955, referred to such abstract hypotheses as overhypotheses.) In a way, these biases due to previous knowledge might seem to be undesirable. After all, wouldn't be it be be

A new inductive learning system, Lab (Learning for ABduction), is presented which acquires abductive rules from a set of training examples. The goal is to find a small knowledge base which, when used abductively, diagnoses the training examples correctly and generalizes well to unseen examples. This contrasts with past systems that inductively learn rules that are used deductively. Each training example is associated with potentially multiple categories (disorders) , instead of one as with typical learning systems. Lab uses a simple hill-climbing algorithm to efficiently build a rule base for a set-covering abductive system. Lab has been experimentally evaluated and compared to other learning systems and an expert knowledge base in the domain of diagnosing brain damage due to stroke. Introduction Most work in symbolic concept acquisition assumes a deductive model of classification in which an example is a member of a concept if it satisfies a logical specification represented in dis...

. We make an attempt to develop a Peircean ontology that is presupposed by propositional logic. The result of this can be seen as a rst step towards linking Peirce's semiotic to his logic of relatives. Familiarity with Peirce's semiotic can be useful, but the thesis of this paper is intelligible without such a background. 1 Introduction The aim of this paper is to develop an ontology presupposed by propositional logic on the basis of Peirce's semiotic ([9]). It will be argued that his denitions of signs involve the meaning of a proposition in the formal logical sense. It will be shown that if, as Peirce maintains, logic is equivalent to semiotic, propositional logic can be derived from a Peircean semiotic. Peirce's classication of signs involves his triads, qualisign-sinsignlegisign, icon-index-symbol, and rheme-dicent-argument. The importance of these triads has been emphasised by most Peirce scholars ([2], [7], [8], [10]). Although Peirce developed also larger systems of si...

Theorem proving is the systematic derivation of a mathematical proof from a set of axioms by the use of rules of inference. We are interested in a related but far less explored problem: the analysis and correction of false conjectures, especially where that correction involves finding a collection of antecedents that, together with a set of axioms, transform non-theorems into theorems. Most failed search trees are huge, and special care is to be taken in order to tackle the combinatorial explosion phenomenon. Fortunately, the planning search space generated by proof plans, see [1], are moderately small. We have explored the possibility of using this technique in the implementation of an abduction mechanism to correct non-theorems.

Formal models of natural language often suer from excessive complexity. A reason for this, we think, may be due to the underlying approach itself. In this paper we introduce a novel, semiotic based model of language which provides us with a simple algorithm for language processing.