Related papers: Binding Contexts as Partitionable Multisets in Abe…
The approach to reasoning about structural operational semantics style specifications supported by the Abella system is discussed. This approach uses lambda tree syntax to treat object language binding and encodes binding related properties…
Abella is an interactive system for reasoning about aspects of object languages that have been formally presented through recursive rules based on syntactic structure. Abella utilizes a two-level logic approach to specification and…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic:…
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…
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…
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…
To correctly use in-context information, language models (LMs) must bind entities to their attributes. For example, given a context describing a "green square" and a "blue circle", LMs must bind the shapes to their respective colors. We…
Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. This ability is central to scientific reasoning, but existing evaluations of relational reasoning in large language models…
Language model users often issue queries that lack specification, where the context under which a query was issued -- such as the user's identity, the query's intent, and the criteria for a response to be useful -- is not explicit. For…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
We present Language-binding Object Graph Network, the first neural reasoning method with dynamic relational structures across both visual and textual domains with applications in visual question answering. Relaxing the common assumption…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
We propose a novel database model whose basic structure is a labeled, directed, acyclic graph with a single root, in which the nodes represent the data sets of an application and the edges represent functional relationships among the data…
Multi-encoder models are a broad family of context-aware neural machine translation systems that aim to improve translation quality by encoding document-level contextual information alongside the current sentence. The context encoding is…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
Treating syntactic equality as a logical connective -- governed by left- and right-introduction rules within the sequent calculus -- offers an elegant and powerful approach to term identity. This treatment of equality allows for the…
In an earlier paper, a new theory of measurefree "conditional" objects was presented. In this paper, emphasis is placed upon the motivation of the theory. The central part of this motivation is established through an example involving a…