A Decidable Confluence Test for Cognitive Models in ACT-R

Computational cognitive modeling investigates human cognition by building detailed computational models for cognitive processes. Adaptive Control of Thought - Rational (ACT-R) is a rule-based cognitive architecture that offers a widely employed framework to build such models. There is a sound and complete embedding of ACT-R in Constraint Handling Rules (CHR). Therefore analysis techniques from CHR can be used to reason about computational properties of ACT-R models. For example, confluence is the property that a program yields the same result for the same input regardless of the rules that are applied. In ACT-R models, there are often cognitive processes that should always yield the same result while others e.g. implement strategies to solve a problem that could yield different results. In this paper, a decidable confluence criterion for ACT-R is presented. It allows to identify ACT-R rules that are not confluent. Thereby, the modeler can check if his model has the desired behavior. The sound and complete translation of ACT-R to CHR from prior work is used to come up with a suitable invariant-based confluence criterion from the CHR literature. Proper invariants for translated ACT-R models are identified and proven to be decidable. The presented method coincides with confluence of the original ACT-R models.Comment: To appear in Stefania Costantini, Enrico Franconi, William Van Woensel, Roman Kontchakov, Fariba Sadri, and Dumitru Roman: "Proceedings of RuleML+RR 2017". Springer LNC

Confluence of CHR Revisited:Invariants and Modulo Equivalence

Abstract simulation of one transition system by another is introduced as a means to simulate a potentially infinite class of similar transition sequences within a single transition sequence. This is useful for proving confluence under invariants of a given system, as it may reduce the number of proof cases to consider from infinity to a finite number. The classical confluence results for Constraint Handling Rules (CHR) can be explained in this way, using CHR as a simulation of itself. Using an abstract simulation based on a ground representation, we extend these results to include confluence under invariant and modulo equivalence, which have not been done in a satisfactory way before.Comment: Pre-proceedings paper presented at the 28th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), Frankfurt am Main, Germany, 4-6 September 2018 (arXiv:1808.03326

Confluence Modulo Equivalence in Constraint Handling Rules

Previous results on proving confluence for Constraint Handling Rules are extended in two ways in order to allow a larger and more realistic class of CHR programs to be considered confluent. Firstly, we introduce the relaxed notion of confluence modulo equivalence into the context of CHR: while confluence for a terminating program means that all alternative derivations for a query lead to the exact same final state, confluence modulo equivalence only requires the final states to be equivalent with respect to an equivalence relation tailored for the given program. Secondly, we allow non-logical built-in predicates such as var/1 and incomplete ones such as is/2, that are ignored in previous work on confluence. To this end, a new operational semantics for CHR is developed which includes such predicates. In addition, this semantics differs from earlier approaches by its simplicity without loss of generality, and it may also be recommended for future studies of CHR. For the purely logical subset of CHR, proofs can be expressed in first-order logic, that we show is not sufficient in the present case. We have introduced a formal meta-language that allows reasoning about abstract states and derivations with meta-level restrictions that reflect the non-logical and incomplete predicates. This language represents subproofs as diagrams, which facilitates a systematic enumeration of proof cases, pointing forward to a mechanical support for such proofs

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 26th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The total of 60 regular papers presented in these volumes was carefully reviewed and selected from 155 submissions. The papers are organized in topical sections as follows: Part I: Program verification; SAT and SMT; Timed and Dynamical Systems; Verifying Concurrent Systems; Probabilistic Systems; Model Checking and Reachability; and Timed and Probabilistic Systems. Part II: Bisimulation; Verification and Efficiency; Logic and Proof; Tools and Case Studies; Games and Automata; and SV-COMP 2020

Verifying procedural programs via constrained rewriting induction

This paper aims to develop a verification method for procedural programs via a transformation into Logically Constrained Term Rewriting Systems (LCTRSs). To this end, we extend transformation methods based on integer TRSs to handle arbitrary data types, global variables, function calls and arrays, as well as encode safety checks. Then we adapt existing rewriting induction methods to LCTRSs and propose a simple yet effective method to generalize equations. We show that we can automatically verify memory safety and prove correctness of realistic functions. Our approach proves equivalence between two implementations, so in contrast to other works, we do not require an explicit specification in a separate specification language