Related papers: Tableaux for Automated Reasoning in Dependently-Ty…

Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…

Propositional linear time temporal logic (LTL) is the standard temporal logic for computing applications and many reasoning techniques and tools have been developed for it. Tableaux for deciding satisfiability have existed since the 1980s.…

Dependent Object Types (DOT) is intended to be a core calculus for modelling Scala. Its distinguishing feature is abstract type members, fields in objects that hold types rather than values. Proving soundness of DOT has been surprisingly…

The logic of hereditary Harrop formulas (HH) has proven useful for specifying a wide range of formal systems. This logic includes a form of hypothetical judgment that leads to dynamically changing sets of assumptions and that is key to…

Logical reasoning is a core challenge in natural language understanding and a fundamental capability of artificial intelligence, underpinning scientific discovery, mathematical theorem proving, and complex decision-making. Despite the…

Many complex scenarios require the coordination of agents possessing unique points of view and distinct semantic commitments. In response, standpoint logic (SL) was introduced in the context of knowledge integration, allowing one to reason…

We propose a new type-theoretic approach to SLD-resolution and Horn-clause logic programming. It views Horn formulas as types, and derivations for a given query as a construction of the inhabitant (a proof-term) for the type given by the…

The use of formal language for deductive logical reasoning aligns well with language models (LMs), where translating natural language (NL) into first-order logic (FOL) and employing an external solver results in a verifiable and therefore…

A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…

While Large Language Models (LLMs) demonstrate remarkable proficiency in semantic understanding, they often struggle to ensure structural consistency and reasoning reliability in complex decision-making tasks that demand rigorous logic.…

Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…

Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…

Table-based reasoning has shown remarkable progress in combining deep models with discrete reasoning, which requires reasoning over both free-form natural language (NL) questions and structured tabular data. However, previous table-based…

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…

Type classes in Haskell are used to implement ad-hoc polymorphism, i.e. a way to ensure both to the programmer and the compiler that a set of functions are defined for a specific data type. All instances of such type classes are expected to…

Ontology learning (OL) is the process of automatically generating an ontological knowledge base from a plain text document. In this paper, we propose a new ontology learning approach and tool, called DLOL, which generates a knowledge base…

We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…

This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…

Syntactic structures used to play a vital role in natural language processing (NLP), but since the deep learning revolution, NLP has been gradually dominated by neural models that do not consider syntactic structures in their design. One…

Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…