Related papers: Case Study: Saturations as Explicit Models in Equa…
In this paper we consider a type system with a universal type $\omega$ where any term (whether open or closed, $\beta$-normalising or not) has type $\omega$. We provide this type system with a realisability semantics where an atomic type is…
We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata…
We carry out a proof theoretic analysis of the wellfoundedness of recursive path orders in an abstract setting. We outline a very general termination principle and extract from its wellfoundedness proof subrecursive bounds on the size of…
There is an increasing interest in applying recent advances in AI to automated reasoning, as it may provide useful heuristics in reasoning over formalisms in first-order, second-order, or even meta-logics. To facilitate this research, we…
Based on our previous work on truly concurrent process algebras APTC, we use it to verify the security protocols. This work (called Secure APTC, abbreviated SAPTC) have the following advantages in verifying security protocols: (1) It has a…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
The Vampire automated theorem prover is extended to output machine-checkable proofs in the Dedukti concrete syntax for the LambdaPi-calculus modulo. This significantly reduces the trusted computing base, and in principle eases proof…
System development is not a linear, one-shot process. It proceeds through refinements and revisions. To support assurance that the system satisfies its requirements, it is desirable that continuous verification can be performed after each…
In structural proof theory, designing and working on large calculi make it difficult to get intuitions about each rule individually and as part of a whole system. We introduce two novel tools to help working on calculi using the approach of…
We present several enumeration results holding in sets of words called neutral and which satisfy restrictive conditions on the set of possible extensions of nonempty words. These formulae concern return words and bifix codes. They…
Mechanistic interpretability often identifies circuits inside Transformer models, but explanations of those circuits are usually validated through examples, ablations, and manual reasoning. This leaves a gap between finding a plausible…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model…
Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint…
Open-textured terms in written rules are typically settled through interpretive argumentation. Ongoing work has attempted to catalogue the schemes used in such interpretive argumentation. But how can the use of these schemes affect the way…
An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and…
The schematic CERES method [8] is a recently developed method of cut elimination for proof schemata, that is a sequence of proofs with a recursive construction. Proof schemata can be thought of as a way to circumvent adding an induction…
Agentic theorem provers often introduce intermediate lemmas, proof sketches, or subgoal decompositions before returning to tactic-level search. This can look like an expensive detour: if proving lemmas is itself hard, why should a learned…
I introduce an approach for automated reasoning in first order set theories that are not finitely axiomatizable, such as $ZFC$, and describe its implementation alongside the automated theorem proving software E. I then compare the results…
Transforming dense, detailed, unstructured text into an interpretable and summarised table, also colloquially known as Text-to-Table generation, is an essential task for information retrieval. Current methods, however, miss out on how and…