Generalised Interpolation by Solving Recursion-Free Horn Clauses

In this paper we present InterHorn, a solver for recursion-free Horn clauses. The main application domain of InterHorn lies in solving interpolation problems arising in software verification. We show how a range of interpolation problems, including path, transition, nested, state/transition and well-founded interpolation can be handled directly by InterHorn. By detailing these interpolation problems and their Horn clause representations, we hope to encourage the emergence of a common back-end interpolation interface useful for diverse verification tools.Comment: In Proceedings HCVS 2014, arXiv:1412.082

Scalable Logic Defined Static Analysis

Logic languages such as Datalog have been proposed as a method for specifying flexible and customisable static analysers. Using Datalog, various classes of static analyses can be expressed precisely and succinctly, requiring fewer lines of code than hand-crafted analysers. In this paradigm, a static analysis specification is encoded by a set of declarative logic rules and an o -the-shelf solver is used to compute the result of the static analysis. Unfortunately, when large-scale analyses are employed, Datalog-based tools currently fail to scale in comparison to hand-crafted static analysers. As a result, Datalog-based analysers have largely remained an academic curiosity, rather than industrially respectful tools. This thesis outlines our e orts in understanding the sources of performance limitations in Datalog-based tools. We propose a novel evaluation technique that is predicated on the fact that in the case of static analysis, the logical specification is a design time artefact and hence does not change during evaluation. Thus, instead of directly evaluating Datalog rules, our approach leverages partial evaluation to synthesise a specialised static analyser from these rules. This approach enables a novel indexing optimisations that automatically selects an optimal set of indexes to speedup and minimise memory usage in the Datalog computation. Lastly, we explore the case of more expressive logics, namely, constrained Horn clause and their use in proving the correctness of programs. We identify a bottleneck in various symbolic evaluation algorithms that centre around Craig interpolation. We propose a method of improving these evaluation algorithms by a proposing a method of guiding theorem provers to discover relevant interpolants with respect to the input logic specification. The culmination of our work is implemented in a general-purpose and highperformance tool called Souffl´e. We describe Souffl´e and evaluate its performance experimentally, showing significant improvement over alternative techniques and its scalability in real-world industrial use cases

Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic

This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL , in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established

High-level characteristics of or-and independent and-parallelism in prolog

Although studies of a number of parallel implementations of logic programming languages are now available, their results are difficult to interpret due to the multiplicity of factors involved, the effect of each of which is difficult to sepárate. In this paper we present the results of a high-level simulation study of or- and independent and-parallelism with a wide selection of Prolog programs that aims to determine the intrinsic amount of parallelism, independently of implementation factors, thus facilitating this separation. We expect this study will be instrumental in better understanding and comparing results from actual implementations, as shown by some examples provided in the paper. In addition, the paper examines some of the issues and tradeoffs associated with the combination of and- and or-parallelism and proposes reasonable solutions based on the simulation data obtained

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book