Related papers: Semantics of Separation-Logic Typing and Higher-or…
We propose a cognitively and linguistically motivated set of sorts for lexical semantics in a compositional setting: the classifiers in languages that do have such pronouns. These sorts are needed to include lexical considerations in a…
Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writing software and solving quantitative problems. We provide a…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
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…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
We consider a simple extension of logic programming where variables may range over goals and goals may be arguments of predicates. In this language we can write logic programs which use goals as data. We give practical evidence that, by…
Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
We describe a mathematical structure that can give extensional denotational semantics to higher-order probabilistic programs. It is not limited to discrete probabilities, and it is compatible with integration in a way the models that have…
In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…
Program logics are a powerful formal method in the context of program verification. Can we develop a counterpart of program logics in the context of language verification? This paper proposes language logics, which allow for statements of…
Choice constructs are an important part of the language of logic programming, yet the study of their semantics has been a challenging task. So far, only two-valued semantics have been studied, and the different proposals for such semantics…
Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…
Compositionality of denotational semantics is an important concern in programming semantics. Mathematical operational semantics in the sense of Turi and Plotkin guarantees compositionality, but seen from the point of view of stateful…
This paper presents a language, Alda, that supports all of logic rules, sets, functions, updates, and objects as seamlessly integrated built-ins. The key idea is to support predicates in rules as set-valued variables that can be used and…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
We present a novel decision procedure for a fragment of separation logic (SL) with arbitrary nesting of separating conjunctions with boolean conjunctions, disjunctions, and guarded negations together with a support for the most common…