Related papers: Polymorphism Meets DHOL
The paper presents a comprehensive analysis of the European AI Act in terms of its logical modalities, with the aim of preparing its formal representation, for example, within the logic-pluralistic Knowledge Engineering Framework and…
The automated theorem prover Leo-III for classical higher-order logic with Henkin semantics and choice is presented. Leo-III is based on extensional higher-order paramodulation and accepts every common TPTP dialect (FOF, TFF, THF),…
In this paper, we propose a novel formalism called Probabilistic Obstruction Temporal Logic (POTL), which extends Obstruction Logic (OL) by incorporating probabilistic elements. POTL provides a robust framework for reasoning about the…
The present dissertation introduces the research project on HOLMS (\textbf{HOL} Light Library for \textbf{M}odal \textbf{S}ystems), a growing modular framework for modal reasoning within the HOL Light proof assistant. To provide an…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
Type inference is an application domain that is a natural fit for logic programming (LP). LP systems natively support unification, which serves as a basic building block of typical type inference algorithms. In particular, polymorphic type…
We present an implementation of a probabilistic first-order logic called TensorLog, in which classes of logical queries are compiled into differentiable functions in a neural-network infrastructure such as Tensorflow or Theano. This leads…
Formally specifying, let alone verifying, properties of systems involving multiple programming languages is inherently challenging. We introduce Heterogeneous Dynamic Logic (HDL), a framework for combining reasoning principles from distinct…
Due to its expressiveness and unambiguous nature, First-Order Logic (FOL) is a powerful formalism for representing concepts expressed in natural language (NL). This is useful, e.g., for specifying and verifying desired system properties.…
We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and…
We present a theory of parameterized dynamic logic, namely DLp, for specifying and reasoning about a rich set of program models based on their transitional behaviours. Different from most dynamic logics that deal with regular expressions or…
A hybrid model involves the cooperation of an interpretable model and a complex black box. At inference, any input of the hybrid model is assigned to either its interpretable or complex component based on a gating mechanism. The advantages…
DatalogMTL is an extension of Datalog with operators from metric temporal logic which has received significant attention in recent years. It is a highly expressive knowledge representation language that is well-suited for applications in…
It is evident that the current state of Large Language Models (LLMs) necessitates the incorporation of external tools. The lack of straightforward algebraic and logical reasoning is well documented and prompted researchers to develop…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
Lambda Prolog is known to be well-suited for expressing and implementing logics and inference systems. We show that lemmas and definitions in such logics can be implemented with a great economy of expression. We encode a higher-order logic…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Multi-methods are a straightforward extension of traditional (single) dynamic dispatch, which is the core of most object oriented languages. With multi-methods, a method call will select an appropriate implementation based on the values of…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
Interpretability of Deep Neural Networks (DNNs) is a growing field driven by the study of vision and language models. Yet, some use cases, like image captioning, or domains like Deep Reinforcement Learning (DRL), require complex modelling,…