Related papers: Transporting Theorems about Typeability in LF Acro…
We present a new strictification method for type-theoretic structures that are only weakly stable under substitution. Given weakly stable structures over some model of type theory, we construct equivalent strictly stable structures by…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages…
Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws,…
In this paper, we take first steps toward developing defeasible reasoning on concepts in KLM framework. We define generalizations of cumulative reasoning system C and cumulative reasoning system with loop CL to conceptual setting. We also…
Phrases are fundamental linguistic units through which humans convey semantics. This study critically examines the capacity of API-based large language models (LLMs) to comprehend phrase semantics, utilizing three human-annotated datasets.…
Semantic typing has become a powerful tool for program verification, applying the technique of logical relations as not only a proof method, but also a device for prescribing program behavior. In recent work, Yao et al. scaled semantic…
Lambda Prolog is known to be well-suited for expressing and implementing logics and inference systems. We show that lemmas and definitions in such logics can be implemented with a great economy of expression. We encode a higher-order logic…
We examine how well the state-of-the-art (SOTA) models used in legal reasoning support abductive reasoning tasks. Abductive reasoning is a form of logical inference in which a hypothesis is formulated from a set of observations, and that…
Metatheorems about type theories are often proven by interpreting the syntax into models constructed using categorical gluing. We propose to use only sconing (gluing along a global section functor) instead of general gluing. The sconing is…
Graph problems are fundamentally challenging for large language models (LLMs). While LLMs excel at processing unstructured text, graph tasks require reasoning over explicit structure, permutation invariance, and computationally complex…
Case-based reasoning networks are machine-learning models that make predictions based on similarity between the input and prototypical parts of training samples, called prototypes. Such models are able to explain each decision by pointing…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
We present TLLC which extends the Two-Level Linear dependent type theory (TLL) with session-based concurrency. Equipped with Martin-L\"{o}f style dependency, the session types of TLLC allow protocols to specify properties of communicated…
Much of the knowledge encoded in transformer language models (LMs) may be expressed in terms of relations: relations between words and their synonyms, entities and their attributes, etc. We show that, for a subset of relations, this…
The logic underlying the Abella proof assistant includes mechanisms for interpreting atomic predicates through fixed point definitions that can additionally be treated inductively or co-inductively. However, the original formulation of the…
Translating formulas of Linear Temporal Logic (LTL) over finite traces, or LTLf, to symbolic Deterministic Finite Automata (DFA) plays an important role not only in LTLf synthesis, but also in synthesis for Safety LTL formulas. The…
Vehicles in public traffic that are equipped with Automated Driving Systems are subject to a number of expectations: Among other aspects, their behavior should be safe, conforming to the rules of the road and provide mobility to their…
This paper introduces a differentiable semantic reasoner, where rules are presented as a relevant set of graph transformations. These rules can be written manually or inferred by a set of facts and goals presented as a training set. While…