Related papers: Logic Column 16: Higher-Order Abstract Syntax: Set…
We develop a class of algebraic interpretations for many-sorted and higher-order term rewriting systems that takes type information into account. Specifically, base-type terms are mapped to \emph{tuples} of natural numbers and higher-order…
Compiler correctness proofs for higher-order concurrent languages are difficult: they involve establishing a termination-preserving refinement between a concurrent high-level source language and an implementation that uses low-level shared…
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…
We show how to give a coherent semantics to programs that are well-specified in a version of separation logic for a language with higher types: idealized algol extended with heaps (but with immutable stack variables). In particular, we…
Prior research in computational argumentation has mainly focused on scoring the quality of arguments, with less attention on explicating logical errors. In this work, we introduce four sets of explainable templates for common informal…
This note clarifies the concept of syntax and semantics and their relationships. Today, a lot of confusion arises from the fact that the word "semantics" is used in different meanings. We discuss a general approach at defining semantics…
We present a first-order logic equipped with an "asymmetric" directed notion of equality, which can be thought of as rewrites between terms, allowing for types to be interpreted as preorders. The logic is equipped with a precise syntactic…
This guideline proposes a systematic and operational annotation framework for representing the structure of legal argumentation in judicial decisions. Grounded in theories of legal reasoning and argumentation, the framework aims to reveal…
This extended abstract gives a brief outline of the connections between the descriptions and variable concepts. Thus, the notion of a concept is extended to include both the syntax and semantics features. The evaluation map in use is…
Text classification with hierarchical labels is a prevalent and challenging task in natural language processing. Examples include assigning ICD codes to patient records, tagging patents into IPC classes, assigning EUROVOC descriptors to…
Though preceding work in computational argument quality (AQ) mostly focuses on assessing overall AQ, researchers agree that writers would benefit from feedback targeting individual dimensions of argumentation theory. However, a large-scale…
These informal notes deal with a number of questions related to sums and integrals in analysis.
Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point…
This letter introduces a new, substantially simplified version of the branching recurrence operation of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proves its equivalence to the old, "canonical" version.
We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC) - a system of higher-order logic modulo theories - and prove its soundness and refutational completeness w.r.t. the standard semantics. As…
Generating logical form equivalents of human language is a fresh way to employ neural architectures where long short-term memory effectively captures dependencies in both encoder and decoder units. The logical form of the sequence usually…
Ontologies often require knowledge representation on multiple levels of abstraction, but description logics (DLs) are not well-equipped for supporting this. We propose an extension of DLs in which abstraction levels are first-class citizens…
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…
Text alignment finds application in tasks such as citation recommendation and plagiarism detection. Existing alignment methods operate at a single, predefined level and cannot learn to align texts at, for example, sentence and document…
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