Related papers: Complexity of Arithmetic in Warded Datalog+-
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
Reasoning is a fundamentally algorithmic task. Yet current work on LLM-based reasoning relies on free-form generation whose theoretical guarantees (soundness, completeness, complexity, optimality) remain poorly understood. We argue that we…
We consider the problem of automated reasoning about dynamically manipulated data structures. The state-of-the-art methods are limited to the unfold-and-match (U+M) paradigm, where predicates are transformed via (un)folding operations…
Starting with early successes in computer vision tasks, deep learning based techniques have since overtaken state of the art approaches in a multitude of domains. However, it has been demonstrated time and again that these techniques fail…
The Semantic Web drives towards the use of the Web for interacting with logically interconnected data. Through knowledge models such as Resource Description Framework (RDF), the Semantic Web provides a unifying representation of richly…
Neither the classical nor intuitionistic logic traditions are perfectly-aligned with the purpose of reasoning about computation, in that neither tradition can permit unconstrained recursive definitions without inconsistency: recursive…
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…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
Artificial Intelligence (AI) increasingly shows its potential to outperform predicate logic algorithms and human control alike. In automatically deriving a system model, AI algorithms learn relations in data that are not detectable for…
We develop game-theoretic semantics (GTS) for the fragment ATL+ of the full Alternating-time Temporal Logic ATL*, essentially extending a recently introduced GTS for ATL. We first show that the new game-theoretic semantics is equivalent to…
Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…
In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of…
In this paper we examine the limitations of Large Language Models (LLMs) for complex reasoning tasks. Although recent works have started to employ formal languages as an intermediate representation for reasoning tasks, they often face…
We consider the one-variable fragment of first-order logic extended with Presburger constraints. The logic is designed in such a way that it subsumes the previously-known fragments extended with counting, modulo counting or cardinality…
Rulelog is a knowledge representation and reasoning language based on logic programming under the well-founded semantics. It is an extension of the language of Flora-2 and so supports inheritance and other object-oriented features, as well…
Reasoning over OWL 2 is a very expensive task in general, and therefore the W3C identified tractable profiles exhibiting good computational properties. Ontological reasoning for many fragments of OWL 2 can be reduced to the evaluation of…
This paper present several refinements of the Datalog +/- framework based on resolution and Datalog-rewriting. We first present a resolution algorithm which is complete for arbitrary sets of tgds and egds. We then show that a technique of…
AI has proven highly successful at urban planning analysis -- learning patterns from data to predict future conditions. The next frontier is AI-assisted decision-making: agents that recommend sites, allocate resources, and evaluate…
Application domains that require considering relationships among objects which have real-valued attributes are becoming even more important. In this paper we propose NeuralLog, a first-order logic language that is compiled to a neural…