Related papers: Bialgebraic Reasoning on Higher-Order Program Equi…
Effectful programs interact in ways that go beyond simple input-output, making compositional reasoning challenging. Existing work has shown that when such programs are ``separate'', i.e., when programs do not interfere with each other, it…
Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates…
First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…
A simple dynamically-typed, (purely) object-oriented language is defined. A structural operational semantics as well as a Hoare-style program logic for reasoning about programs in the language in multiple notions of correctness are given.…
Properties such as provable security and correctness for randomized programs are naturally expressed relationally as approximate equivalences. As a result, a number of relational program logics have been developed to reason about such…
A propositional logic program $P$ may be identified with a $P_fP_f$-coalgebra on the set of atomic propositions in the program. The corresponding $C(P_fP_f)$-coalgebra, where $C(P_fP_f)$ is the cofree comonad on $P_fP_f$, describes…
Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this…
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…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent computations where code usage plays a central role. The theory of program equivalence for modal and coeffectful languages, however, is…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
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…
In this article, we develop a new and somewhat unexpected connection between higher-order model-checking and linear logic. Our starting point is the observation that once embedded in the relational semantics of linear logic, the Church…
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…
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…
Logic programming is sometimes described as relational programming: a paradigm in which the programmer specifies and composes n-ary relations using systems of constraints. An advanced logic programming environment will provide tools that…
The relationship between communicated language and intended meaning is often probabilistic and sensitive to context. Numerous strategies attempt to estimate such a mapping, often leveraging recursive Bayesian models of communication. In…
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…
Large language models (LLMs) are increasingly used in domains where causal reasoning matters, yet it remains unclear whether their judgments reflect normative causal computation, human-like shortcuts, or brittle pattern matching. We…
Both syntax-phonology and syntax-semantics interfaces in Higher Order Grammar (HOG) are expressed as axiomatic theories in higher-order logic (HOL), i.e. a language is defined entirely in terms of provability in the single logical system.…