Related papers: Paraconsistent Reasoning via Quantified Boolean Fo…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
Symmetries have been exploited successfully within the realms of SAT and QBF to improve solver performance in practical applications and to devise more powerful proof systems. As a first step towards extending these advancements to the…
Conditional question answering (CQA) is an important task that aims to find probable answers and identify missing conditions. Existing approaches struggle with CQA due to two challenges: (1) precisely identifying necessary conditions and…
Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the…
A classic result due to Schaefer (1978) classifies all constraint satisfaction problems (CSPs) over the Boolean domain as being either in $\mathsf{P}$ or $\mathsf{NP}$-hard. This paper considers a promise-problem variant of CSPs called…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…
We present a novel formalization of counterfactual conditionals in a quantified modal logic. Counterfactual conditionals play a vital role in ethical and moral reasoning. Prior work has shown that moral reasoning systems (and more…
The requirement for identifying accurate system representations has not only been a challenge to fulfill, but it has compromised the scalability of formal methods, as the resulting models are often too complex for effective decision making…
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as…
This thesis develops a framework for formalizing reasoning about specifications of systems written in LF. This formalization centers around the development of a reasoning logic that can express the sorts of properties which arise in…
Signed networks provide a principled framework for representing systems in which interactions are not merely present or absent but qualitatively distinct: friendly or antagonistic, supportive or conflicting, excitatory or inhibitory. This…
We introduce new semi-algebraic proof systems for Quantified Boolean Formulas (QBF) analogous to the propositional systems Nullstellensatz, Sherali-Adams and Sum-of-Squares. We transfer to this setting techniques both from the QBF…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
Existing datasets that contain boolean questions, such as BoolQ and TYDI QA , provide the user with a YES/NO response to the question. However, a one word response is not sufficient for an explainable system. We promote explainability by…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
This paper proposes a new category theoretic account of equationally axiomatizable classes of algebras. Our approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered…
Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when…
This paper investigates the algorithmic safety verification problem of infinite-state parameterized concurrent programs over a rich set of communication topologies. The goal is to automatically produce a proof of correctness in the form of…