Related papers: FOLE: The First-order Logical Environment
Transformer architectures have achieved great success in solving natural language tasks, which learn strong language representations from large-scale unlabeled texts. In this paper, we seek to go further beyond and explore a new logical…
We investigate a class of first-order temporal-epistemic logics for reasoning about multi-agent systems. We encode typical properties of systems including perfect recall, synchronicity, no learning, and having a unique initial state in…
Foundation models offer a new opportunity to redesign existing systems and workflows with a new AI first perspective. However, operationalizing this opportunity faces several challenges and tradeoffs. The goal of this article is to offer an…
Popular machine learning approaches forgo second-order information due to the difficulty of computing curvature in high dimensions. We present FOSI, a novel meta-algorithm that improves the performance of any base first-order optimizer by…
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…
DOLCE, the first top-level (foundational) ontology to be axiomatized, has remained stable for twenty years and today is broadly used in a variety of domains. DOLCE is inspired by cognitive and linguistic considerations and aims to model a…
The paper considers the class of information systems capable of solving heuristic problems on basis of formal theory that was termed modal and vector theory of formal intelligent systems (FIS). The paper justifies the construction of FIS…
In this paper we considered the extension of the First-order Logic (FOL) by Bealer's intensional abstraction operator. Contemporary use of the term 'intension' derives from the traditional logical Frege-Russell's doctrine that an idea…
Computability logic (CoL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth…
Artificial Intelligence aims to provide computer programs with commonsense knowledge to reason about our world. This paper offers a new practical approach towards automated commonsense reasoning with first-order logic (FOL) ontologies. We…
Recent Large Reasoning Models (LRMs) like DeepSeek-R1 have demonstrated remarkable success in complex reasoning tasks, exhibiting human-like patterns in exploring multiple alternative solutions. Upon closer inspection, however, we uncover a…
First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type…
The present article is a brief informal survey of computability logic --- the game-semantically conceived formal theory of computational resources and tasks. This relatively young nonclassical logic is a conservative extension of classical…
Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…
Intelligent systems in an open world must reason about many interacting entities related to each other in diverse ways and having uncertain features and relationships. Traditional probabilistic languages lack the expressive power to handle…
Lin and Zhaos theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the…
A formal context consists of objects, properties, and the incidence relation between them. Various notions of concepts defined with respect to formal contexts and their associated algebraic structures have been studied extensively,…
Separation logic is a concise method for specifying programs that manipulate dynamically allocated storage. Partially inspired by separation logic, Implicit Dynamic Frames has recently been proposed, aiming at first-order tool support. In…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
This paper presents a distributed agent-based automated theorem proving framework based on order-sorted first-order logic. Each agent in our framework has its own knowledge base, communicating to its neighboring agent(s) using…