Related papers: Bounded Modal Logic
We give a new presentation of interactive realizability with a more explicit syntax. Interactive realizability is a realizability semantics that extends the Curry-Howard correspondence to (sub-)classical logic, more precisely to first-order…
Classical mathematical models used in the semantics of programming languages and computation rely on idealized abstractions such as infinite-precision real numbers, unbounded sets, and unrestricted computation. In contrast, concrete…
The starting point of this work is the observation that the Curry-Howard isomorphism, relating types and propositions, programs and proofs, composition and cut, extends to the correspondence of program fusion and cut elimination. This…
We propose a logic of interactive proofs as a framework for an intuitionistic foundation for interactive computation, which we construct via an interactive analog of the Goedel-McKinsey-Tarski-Artemov definition of Intuitionistic Logic as…
Combinatorial sequential decision making problems are typically modeled as mixed integer linear programs (MILPs) and solved via branch and bound (B&B) algorithms. The inherent difficulty of modeling MILPs that accurately represent…
This paper introduces higher-order (``nested") Kripke models, a generalization of Kripke models that is remarkably close to Kripke's original idea -- both mathematically and conceptually. Standard models are now $0$-ary models, whereas…
Probabilistic behavior is omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of various reasons, like uncertain environments, or fundamental properties of nature. In this paper, we…
Inquisitive modal logic, InqML, in its epistemic incarnation, extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. We use the natural notion of…
We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…
The $\lambda\mu$-calculus plays a central role in the theory of programming languages as it extends the Curry-Howard correspondence to classical logic. A major drawback is that it does not satisfy B\"ohm's Theorem and it lacks the…
Dummett's logic LC is intuitionistic logic extended with Dummett's axiom: for every two statements the first implies the second or the second implies the first. We present a natural deduction and a Curry-Howard correspondence for…
This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…
We introduce Nominal Matching Logic (NML) as an extension of Matching Logic with names and binding following the Gabbay-Pitts nominal approach. Matching logic is the foundation of the $\mathbb{K}$ framework, used to specify programming…
We present natural deduction systems and associated modal lambda calculi for the necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in the dual-context style: they feature two distinct zones of…
A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive…
This article develops a novel framework for modal logic based on the idea of stratified actualization, rather than the classical model of global possible worlds. Traditional Kripke semantics treat modal operators as quantification over…
Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model-theoretic structures; the latter represents meaning as vectors in high-dimensional spaces shaped…
Heyting-Lewis Logic is the extension of intuitionistic propositional logic with a strict implication connective that satisfies the constructive counterparts of axioms for strict implication provable in classical modal logics. Variants of…
We explore various semantic understandings of dual intuitionistic logic by exploring the relationship between co-Heyting algebras and topological spaces. First, we discuss the relevant ideas in the setting of Heyting algebras and…
Program transformations are widely used in synthesis, optimization, and maintenance of software. Correctness of program transformations depends on preservation of some important properties of the input program. By regarding programs as…