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A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
Explanations for description logic (DL) entailments provide important support for the maintenance of large ontologies. The "justifications" usually employed for this purpose in ontology editors pinpoint the parts of the ontology responsible…
PDDL+ is an extension of PDDL2.1 which incorporates fully-featured autonomous processes and allows for better modelling of mixed discrete-continuous domains. Unlike PDDL2.1, PDDL+ lacks a logical semantics, relying instead on…
Disjunctive Logic Programming (DLP) is a very expressive formalism: it allows for expressing every property of finite structures that is decidable in the complexity class SigmaP2 (= NP^NP). Despite this high expressiveness, there are some…
The uses of machine learning (ML) have snowballed in recent years. In many cases, ML models are highly complex, and their operation is beyond the understanding of human decision-makers. Nevertheless, some uses of ML models involve…
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…
The present paper provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. Dynamic epistemic logic is one of the best known members of a family of logical systems which…
In text classification, dictionaries can be used to define human-comprehensible features. We propose an improvement to dictionary features called smoothed dictionary features. These features recognize document contexts instead of n-grams.…
We describe Imandra, a modern computational logic theorem prover designed to bridge the gap between decision procedures such as SMT, semi-automatic inductive provers of the Boyer-Moore family like ACL2, and interactive proof assistants for…
For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular. If L contains a non-regular language, PDL[L] can express non-regular…
Terminological knowledge representation systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). We analyze from a theoretical point of view a TKRS whose…
The objective of this proposal is to bridge the gap between Deep Learning (DL) and System Dynamics (SD) by developing an interpretable neural system dynamics framework. While DL excels at learning complex models and making accurate…
Large language models~(LLMs) present an intriguing avenue of exploration in the domain of formal theorem proving. Nonetheless, the full utilization of these models, particularly in terms of demonstration formatting and organization, remains…
Deep Learning (DL) models processing images to recognize the health state of large infrastructure components can exhibit biases and rely on non-causal shortcuts. eXplainable Artificial Intelligence (XAI) can address these issues but…
The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…
Cyber-physical systems are inherently complex due to their connection between software and the physical world. Iterative design reduces their complexity, but increases the need to repeatedly recheck their safety in full after every change.…
Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability properties from the differential inclusion. Their…
Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has…
I present the most fundamental features of an implemented system designed to manipulate representations of regular languages. The system is structured into two layers, allowing regular languages to be represented in an increasingly compact,…
Modern separation logics allow one to prove rich properties of intricate code, e.g. functional correctness and linearizability of non-blocking concurrent code. However, this expressiveness leads to a complexity that makes these logics…