Related papers: A Splitting Set Theorem for Epistemic Specificatio…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel…
We show that propositional logic and its extensions can support answer-set programming in the same way stable logic programming and disjunctive logic programming do. To this end, we introduce a logic based on the logic of propositional…
Prior work has combined chain-of-thought prompting in large language models (LLMs) with programmatic representations to perform effective and transparent reasoning. While such an approach works well for tasks that only require forward…
Answer set programming - the most popular problem solving paradigm based on logic programs - has been recently extended to support uninterpreted function symbols. All of these approaches have some limitation. In this paper we propose a…
In recent research on non-monotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P union R and Q union R have the same answer sets for any other program R. This…
Understanding human instructions to identify the target objects is vital for perception systems. In recent years, the advancements of Large Language Models (LLMs) have introduced new possibilities for image segmentation. In this work, we…
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…
In this paper we introduce Epistemic Strategy Logic (ESL), an extension of Strategy Logic with modal operators for individual knowledge. This enhanced framework allows us to represent explicitly and to reason about the knowledge agents have…
Recent work to enhance data partitioning strategies for more realistic model evaluation face challenges in providing a clear optimal choice. This study addresses these challenges, focusing on morphological segmentation and synthesizing…
Without prior knowledge, distinguishing different languages may be a hard task, especially when their borders are permeable. We develop an extension of spectral clustering -- a powerful unsupervised classification toolbox -- that is shown…
Motivated by applications in declarative data analysis, we study $\mathit{Datalog}_{\mathbb{Z}}$---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two…
Epistemic reasoning requires agents to infer the state of the world from partial observations and information about other agents' knowledge. Prior work evaluating LLMs on canonical epistemic puzzles interpreted their behavior through a…
We introduce SMProbLog, a generalization of the probabilistic logic programming language ProbLog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly…
Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for…
We present in this paper a reformulation of the usual set-theoretical semantics of the description logic $\mathcal{ALC}$ with general TBoxes by using categorical language. In this setting, $\mathcal{ALC}$ concepts are represented as…
We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence…
We develop an extensional semantics for higher-order logic programs with negation, generalizing the technique that was introduced in [Bezem99,Bezem01] for positive higher-order programs. In this way we provide an alternative extensional…
This paper provides a complete suite of axioms for a version of set theory that I call Explication. Explication borrows from the two most prominent existing systems of set theory. Explication starts with class variables. After several…
Program slicing has been mainly studied in the context of imperative languages, where it has been applied to a wide variety of software engineering tasks, like program understanding, maintenance, debugging, testing, code reuse, etc. This…