LPAR-21S: Papers with Abstracts

Abstract. We outline the implementation of a query compiler for relational queries that generates query plans with respect to a database schema, that is, a set of arbitrary first-order constraints, and a distinguished subset of predicate symbols from the underlying signature that correspond to access paths. The compiler is based on a variant of the Craig interpolation theorem, with reasoning realized via a modified analytic tableau proof procedure. This procedure decouples the generation of candidate plans that are interpolants from the tableau proof procedure, and applies A*-based search with respect to an external cost model to arbitrate among the alternative candidate plans. The tableau procedure itself is implemented as a virtual machine that operates on a compiled and optimized byte-code that faithfully implements reasoning with respect to the database schema constraints and a user query.

Abstract. Leo-III is an automated theorem prover for (polymorphic) higher-order logic which supports all common TPTP dialects, including THF, TFF and FOF as well as their rank-1 polymorphic derivatives. It is based on a paramodulation calculus with ordering constraints and, in tradition of its predecessor LEO-II, heavily relies on cooperation with external first-order theorem provers.
Unlike LEO-II, asynchronous cooperation with typed first-order provers and an agent-based internal cooperation scheme is supported. In this paper, we sketch Leo-III's underlying calculus, survey implementation details and give examples of use.

Abstract. Ontologies are notoriously hard to define, express and reason about. Many tools have been developed to ease the debugging and the reasoning process with ontologies, however they often lack accessibility and formalisation. A visual representation language, concept diagrams, was developed for expressing and reasoning about ontologies in an accessible way. Indeed, empirical studies show that concept diagrams are cognitively more accessible to users in ontology debugging tasks. In this paper we answer the question of “ How can concept diagrams be used to reason about inconsistencies and incoherence of ontologies?”. We do so by formalising a set of inference rules for concept diagrams that enables stepwise verification of the inconsistency and/or incoherence of a set of ontology axioms. The design of inference rules is driven by empirical evidence that concise (merged) diagrams are easier to comprehend for users than a set of lower level diagrams that offer a one-to-one translation of OWL ontology axioms into concept diagrams. We prove that our inference rules are sound, and exemplify how they can be used to reason about inconsistencies and incoherence. Finally, we indicate how our rules can serve as a foundation for new rules required when representing ontologies in diverse new domains.

Abstract. We present fully formalized proofs of some central theorems from combinatorics. These are Dilworth's decomposition theorem, Mirsky's theorem, Hall's marriage theorem and the Erdős-Szekeres theorem. Dilworth's decomposition theorem is the key result among these. It states that in any finite partially ordered set (poset), the size of a smallest chain cover and a largest antichain are the same. Mirsky's theorem is a dual of Dilworth's decomposition theorem, which states that in any finite poset, the size of a smallest antichain cover and a largest chain are the same. We use Dilworth's theorem in the proofs of Hall's Marriage theorem and the Erdős-Szekeres theorem. The combinatorial objects involved in these theorems are sets and sequences. All the proofs are formalized in the Coq proof assistant. We develop a library of definitions and facts that can be used as a framework for formalizing other theorems on finite posets.

Abstract. Crowdsourcing promises to quasi-automate tasks that cannot be automated otherwise. Success stories like natural language translation or recognition of cats in images show that carefully crafted crowdsourcing tasks solve large problem instances which could not be solved otherwise. To utilize crowdsourcing, one has to define the problem in a way that is easy to split into small tasks, that the tasks are easy to solve for humans and hard to solve for a machine, and that the machine can efficiently check if the solution is correct.

In this paper we discuss a novel approach of using crowdsourcing to assist software verification. We argue that Horn clauses form a good base for crowdsourcing since they are easy to subdivide, and that logic abduction is a suitable task since it is hard to find abductive inferences for Horn clauses automatically, but it is easy to check if an inference makes a Horn clause valid. We describe a prototype implementation, we show how crowdsourcing integrates in the verification process, and present preliminary results.

Abstract. Gossip protocols deal with a group of communicating agents, each holding some private information, and aim at arriving at a situation in which all the agents know each other secrets. Distributed epistemic gossip protocols are particularly simple distributed programs that use as guards formulas from an epistemic logic. We showed recently that the implementability of these distributed gossip protocols and the problems of their partial correctness and termination are decidable, but the problem of decidability of their fair termination was left open. We study here rule-fair and agent-fair termination of these protocols and show that both properties are decidable.

Abstract. The paper looks at tooling aspects of transforming C# programs into symbolic transducers with branching rules (BSTs). The latter are used for describing list comprehensions that incorporate loop-carried state. One concrete application is log analysis where input streams of data are transformed into output streams of data via intermediate pipelines of transducers. The paper presents algorithms for translating C# to BSTs, and for exposing control state in BSTs.

Abstract. While interactive proof assistants for higher-order logic (HOL) commonly admit reasoning within rich type systems, current theorem provers for HOL are mainly based on simply typed lambda-calculi and therefore do not allow such flexibility. In this paper, we present modifications to the higher-order automated theorem prover Leo-III for turning it into a reasoning system for rank-1 polymorphic HOL.
To that end, a polymorphic version of HOL and a suitable paramodulation-based calculus are sketched. The implementation is evaluated using a set of polymorphic TPTP THF problems.

Abstract. Automated reasoning systems such as theorem provers often employ interaction or cooperation with further reasoning software. Whereas in most cases the concrete choice of cooperating software is, to some extent, irrelevant, these systems are nevertheless often rigid in practice due to compatibility issues. In order to support more flexible cooperation schemes, a machine-readable description format for automated reasoning systems' capabilities is proposed. Additionally, a simple HTTP-based protocol for system and capability discovery is outlined. Both the format and the protocol are designed to be simple, extensible and easy to use with none to minor modifications for existing reasoning systems.

Abstract. In this paper we present an approach to reasoning with large theories which is based on the abstraction-refinement framework.
The proposed approach consists of the following approximations: the over-approximation, the under-approximation, and their combination.

Abstract. This paper describes initial experiments using the set of support strategy to improve how a saturation-based theorem prover performs theory reasoning with explicit theory axioms. When dealing with theories such as arithmetic, modern automated theorem provers often resort to adding explicit theory axioms, for example, x+y = y+x. Reasoning with such axioms can be explosive. However, little has been done to explore methods that mitigate the negative impact of theory axioms on saturation-based reasoning. The set of support strategy requires that all inferences involve a premise with an ancestor in a so-called set of support,
initially taken to be a subset of the input clauses, usually those corresponding to the goal. This leads to completely goal orientated reasoning but is incomplete for practical reasoning (e.g. in the presence of ordering constraints). The idea of this paper is to apply the set of support strategy to theory axioms only, and then to explore the effect of allowing some limited reasoning within this set. The suggested approach is implemented and evaluated within the VAMPIRE theorem prover.