The marking problem consists in assessing typed student answers for correctness with respect to a ground truth solution. This is a challenging problem that we seek to tackle using a combination of a computer algebra system, an SMT solver and a term rewriting system. A Large Language Model is used to interpret and remove errors from student responses and rewrite these in a machine readable format. Once formalized and language-aligned, the next step then consists in applying automated reasoning techniques for assessing student solution correctness. We consider two methods of automated theorem proving: off-the-shelf SMT solving and term rewriting systems tailored for physics problems involving trigonometric expressions. The development of the term rewrite system and establishing termination and confluence properties was not trivial, and we describe it in some detail in the paper. We evaluate our system on a rich pool of over 1500 real-world student exam responses from the 2023 Australian Physics Olympiad.

We introduce Natlog, a lightweight Logic Programming language, sharing Prolog's unification-driven execution model, but with a simplified syntax and semantics. Our proof-of-concept Natlog implementation is tightly embedded in the Python-based deep-learning ecosystem with focus on content-driven indexing of ground term datasets. As an overriding of our symbolic indexing algorithm, the same function can be delegated to a neural network, serving ground facts to Natlog's resolution engine. Our open-source implementation is available as a Python package at https://pypi.org/project/natlog/ .

A version of the situation calculus in which situations are represented as first-order terms is presented. Fluents can be computed from the term structure, and actions on the situations correspond to rewrite rules on the terms. Actions that only depend on or influence a subset of the fluents can be described as rewrite rules that operate on subterms of the terms in some cases. If actions are bidirectional then efficient completion methods can be used to solve planning problems. This representation for situations and actions is most similar to the fluent calculus of Thielscher \cite{Thielscher98}, except that this representation is more flexible and more use is made of the subterm structure. Some examples are given, and a few general methods for constructing such sets of rewrite rules are presented. This paper was submitted to FSCD 2020 on December 23, 2019.

Inspired by the magic sets for Datalog, we present a novel goal-driven approach for answering queries over terminating existential rules with equality (aka TGDs and EGDs). Our technique improves the performance of query answering by pruning the consequences that are not relevant for the query. This is challenging in our setting because equalities can potentially affect all predicates in a dataset. We address this problem by combining the existing singularization technique with two new ingredients: an algorithm for identifying the rules relevant to a query and a new magic sets algorithm. We show empirically that our technique can significantly improve the performance of query answering, and that it can mean the difference between answering a query in a few seconds or not being able to process the query at all.

Consequence-based calculi are a family of reasoning algorithms for description logics (DLs), and they combine hypertableau and resolution in a way that often achieves excellent performance in practice. Up to now, however, they were proposed for either Horn DLs (which do not support disjunction), or for DLs without counting quantifiers. In this paper we present a novel consequence-based calculus for SRIQ — a rich DL that supports both features. This extension is non-trivial since the intermediate consequences that need to be derived during reasoning cannot be captured using DLs themselves. The results of our preliminary performance evaluation suggest the feasibility of our approach in practice.