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

Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms,heuristics and threshold phenomena. Recent work on heuristics, and the satisfiability threshold has centered

Abstract. Reiter’s default logic formalizes nonmonotonic reasoning using default assumptions. The semantics of a given instance of default logic is based on a fixpoint equation defining an extension. Three different reasoning problems arise in the context of default logic, namely the existence of an extension, the presence of a given formula in an extension, and the occurrence of a formula in all extensions. Since the end of 1980s, several complexity results have been published concerning these default reasoning problems for different syntactic classes of formulas. We derive in this paper a complete classification of default logic reasoning problems by means of universal algebra tools using Post’s clone lattice. In particular we prove a trichotomy theorem for the existence of an extension, classifying this problem to be either polynomial, NP-complete, or Σ2P-complete, depending on the set of underlying Boolean connectives. We also prove similar trichotomy theorems for the two other algorithmic problems in connection with default logic reasoning. 1

Abduction is a fundamental form of nonmonotonic reasoning, which aims at finding explanations for observed manifestations. Applications of this process range from car configuration to medical diagnosis. We study here its computational complexity in the case where the application domain is described by a propositional knowledge base. Building on previous results, we completely classify the complexity for every possible local restriction on the knowledge base and under various restrictions on hypotheses and manifestations. It turns out that depending on the restrictions, the problem is polynomial-time solvable, NP-complete, coNP-complete, or Σ P 2-complete. Based on these results, we are able to give an a posteriori justification of what makes propositional abduction hard when, though, the knowledge base allows for efficient satisfiability testing and deduction. This justification is very simple and intuitive, but it reveals that no nontrivial class of abduction problems is tractable. Indeed, essentially the absence of “causal ” links or the impossibility to specify conflicting hypotheses is required for obtaining tractability.

Abduction is an important method of non-monotonic reasoning with many applications in AI and related topics. In this paper, we concentrate on propositional abduction, where the background knowledge is given by a propositional formula. Decision problems of great interest are the existence and the relevance problems. The complexity of these decision problems has been systematically studied while the counting complexity of propositional abduction has remained obscure. The goal of this work is to provide a comprehensive analysis of the counting complexity of propositional abduction in various classes of theories. 1

We study the computational complexity of Boolean constraint satisfaction problems with cardinality constraint. A Galois connection between clones and co-clones has received a lot of attention in the context of complexity considerations for constraint satisfaction problems. This connection does not seem to help when considering constraint satisfaction problems that support in addition a cardinality constraint. We prove that a similar Galois connection, involving a weaker closure operator and partial polymorphisms, can be applied to such problems. Thus, we establish dichotomies for the decision as well as for the counting problems in Schaefer’s framework.

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Abduction [12] is a well-known form of common-sense reasoning that has been widely exploited in Artificial Intelligence applications, including formalization of Diagnostic Reasoning [13] and Scene Interpretation [14]. Abduction has been also proposed as a logical tool for formalizing hypothetical reasoning in E-Commerce [7], Negotiation

Abstract—In semantic matchmaking processes it is often useful, when the obtained match is not full, to provide explanations for the mismatch, to leverage further interaction and/or modifying the request. To this aim, Abduction in Description Logics has been studied, though —till now — on rather inexpressive languages. In this paper we present a new method for computing Abduction over complex concept descriptions in the expressive Description Logic SH. Our proposal divides the abduced concept in pieces, which allow for direct and concise explanations. The approach exploits information within a prefixed tableau to compute solutions that take into account the structure of a formula. Hypotheses are pieces of a formula to be added inside the quantifiers of a complex concept description and not just added as outermost conjunctions. we propose suitable definitions of the problem, algorithms and calculus. we also give some hints on how to fruitfully use the proposed technique to provide rankings in the matchmaking process. I.

We present an analysis which takes as its input a sequential program, augmented with annotations indicating potential parallelization opportunities, and a sequential proof, written in separation logic, and produces a correctly-synchronized parallelized program and proof of that program. Unlike previous work, ours is not a simple independence analysis that admits parallelization only when threads do not interfere; rather, we insert synchronization to preserve dependencies in the sequential program that might be violated by a naïve translation. Separation logic allows us to parallelize fine-grained patterns of resource-usage, moving beyond straightforward points-to analysis. The sequential proof need only represent shape properties, meaning we can handle complex algorithms without verifying every aspect of their behavior. Our analysis works by using the sequential proof to discover dependencies between different parts of the program. It leverages these discovered dependencies to guide the insertion of synchronization primitives into the parallelized program, and to ensure that the resulting parallelized program satisfies the same specification as the original sequential program, and exhibits the same sequential behavior. Our analysis is built using frame inference and abduction, two techniques supported by an increasing number of separation logic tools.