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The purpose of this paper is to develop further the main concepts of Phenomena Dynamic Logic (P-DL) and Cognitive Dynamic Logic (C-DL), presented in the previous paper. The specific character of these logics is in matching vagueness or…
The purpose of this paper is to outline a simple set of axioms for basic set theory from which most fundamental facts can be derived. The key to the whole project is a new axiom of set theory which I dubbed "The Law of Extremes". It allows…
Large Language Models (LLMs) achieve strong performance in analyzing and generating text, yet they struggle with explicit, transparent, and verifiable reasoning over complex texts such as those containing debates. In particular, they lack…
We express Brewka's prioritised default logic (PDL) as argumentation using ASPIC+. By representing PDL as argumentation and designing an argument preference relation that takes the argument structure into account, we prove that the…
The Minimum Description Length (MDL) principle selects the model that has the shortest code for data plus model. We show that for a countable class of models, MDL predictions are close to the true distribution in a strong sense. The result…
Ontologies are an important tool for structuring domain knowledge, but their development is a complex task that requires significant modelling and domain expertise. Ontology learning, aimed at automating this process, has seen advancements…
Answer-set programming (ASP) has emerged recently as a viable programming paradigm. We describe here an ASP system, DATALOG with constraints or DC, based on non-monotonic logic. Informally, DC theories consist of propositional clauses…
There is a growing interest in applying pre-trained large language models (LLMs) to planning problems. However, methods that use LLMs directly as planners are currently impractical due to several factors, including limited correctness of…
Hypothetical Datalog is based on an intuitionistic semantics rather than on a classical logic semantics, and embedded implications are allowed in rule bodies. While the usual implication (i.e., the neck of a Horn clause) stands for…
We introduce stratified labelings as a novel semantical approach to abstract argumentation frameworks. Compared to standard labelings, stratified labelings provide a more fine-grained assessment of the controversiality of arguments using…
Fixing static analysis alerts in source code with Large Language Models (LLMs) is becoming increasingly popular. However, LLMs often hallucinate and perform poorly for complex and less common alerts. Retrieval-augmented generation (RAG)…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained with the help of proofs of the computed consequences. For ontologies based on Description Logic (DL), we have put this advantage into practice…
We present an end-to-end framework for planning supported by verifiers. An orchestrator receives a human specification written in natural language and converts it into a PDDL (Planning Domain Definition Language) model, where the domain and…
State-of-the-art Datalog engines include expressive features such as ADTs (structured heap values), stratified aggregation and negation, various primitive operations, and the opportunity for further extension using FFIs. Current…
We investigate the expressive power of the two main kinds of program logics for complex, non-regular program properties found in the literature: those extending propositional dynamic logic (PDL), and those extending the modal mu-calculus.…
The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension…
To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015 Recent advances in knowledge compilation introduced techniques to compile \emph{positive} logic programs into propositional logic, essentially exploiting…
Predicates are foundational components in data analysis systems. However, modern workloads increasingly involve unstructured documents, which demands semantic understanding, beyond traditional value-based predicates. Given enormous…
The Abstraction and Reasoning Corpus (ARC) is a challenging benchmark, introduced to foster AI research towards human-level intelligence. It is a collection of unique tasks about generating colored grids, specified by a few examples only.…
Supervised dictionary learning (SDL) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. The goal of SDL is to learn a…