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The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
Intersection types are an essential tool in the analysis of operational and denotational properties of lambda-terms and functional programs. Among them, non-idempotent intersection types provide precise quantitative information about the…
The concurrent logical framework CLF is an extension of the logical framework LF designed to specify concurrent and distributed languages. While it can be used to define a variety of formalisms, reasoning about such languages within CLF has…
Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics. The main syntactic constructs of D-logic are terms, formulas and definitions. A definition…
The use of formal language for deductive logical reasoning aligns well with language models (LMs), where translating natural language (NL) into first-order logic (FOL) and employing an external solver results in a verifiable and therefore…
Virtually all verification techniques using formal methods rely on the availability of a formal specification, which describes the design requirements precisely. However, formulating specifications remains a manual task that is notoriously…
We present a logical framework for the verification of relational properties in imperative programs. Our work is motivated by relational properties which come from security applications and often require reasoning about formulas with…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
Many recent analyses for conventional imperative programs begin by transforming programs into logic programs, capitalising on existing LP analyses and simple LP semantics. We propose using logic programs as an intermediate program…
Modern logics of dependence and independence are based on team semantics, which means that formulae are evaluated not on a single assignment of values to variables, but on a set of such assignments, called a team. This leads to high…
Linear Temporal Logic (LTL) is a widely used specification framework for linear time properties of systems. The standard approach for verifying such properties is by transforming LTL formulae to suitable $\omega$-automata and then applying…
Verification of higher-order probabilistic programs is a challenging problem. We present a verification method that supports several quantitative properties of higher-order probabilistic programs. Usually, extending verification methods to…
Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also…
As originally proposed, type classes provide overloading and ad-hoc definition, but can still be understood (and implemented) in terms of strictly parametric calculi. This is not true of subsequent extensions of type classes. Functional…
Logical reasoning is a core challenge in natural language understanding and a fundamental capability of artificial intelligence, underpinning scientific discovery, mathematical theorem proving, and complex decision-making. Despite the…
A finitary propositional logic can be given an algebraic reading in two different ways: by translating formulas into equations and logical rules into quasi-equations, or by translating logical rules directly into equations. The former type…
We propose a new type-theoretic approach to SLD-resolution and Horn-clause logic programming. It views Horn formulas as types, and derivations for a given query as a construction of the inhabitant (a proof-term) for the type given by the…
Interpretable text representations should expose coordinates that are not only predictive, but also meaningful enough for independent auditors to apply. Existing discriminative representations often use anonymous embedding directions, while…
The Lax Logical Framework, LLFP, was introduced, by a team including the last two authors, to provide a conceptual framework for integrating different proof development tools, thus allowing for external evidence and for postponing,…