Related papers: Logic of fusion
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Any set of truth-functional connectives has sequent calculus rules that can be generated systematically from the truth tables of the connectives. Such a sequent calculus gives rise to a multi-conclusion natural deduction system and to a…
Under the Curry--Howard isomorphism, the syntactic structure of programs can be modeled using birelational Kripke structures equipped with intuitionistic and modal relations. Intuitionistic relations capture scoping through persistence,…
This is a survey of {\lambda}-calculi that, through the Curry-Howard isomorphism, correspond to constructive modal logics. We cover the prehistory of the subject and then concentrate on the developments that took place in the 1990s and…
The goal of this note is to compare two notions, one coming from the theory of rewrite systems and the other from proof theory: confluence and cut elimination. We show that to each rewrite system on terms, we can associate a logical system:…
We present an approach to modeling computational calculi using higher category theory. Specifically we present a fully abstract semantics for the pi-calculus. The interpretation is consistent with Curry-Howard, interpreting terms as typed…
The Curry-Howard Correspondence has a long history, and still is a topic of active research. Though there are extensive investigations into the subject, there doesn't seem to be a definitive formulation of this result in the level of…
In a previous paper (of which this is a prosecution) we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended…
This paper will focus on the process of 'fusing' several observations or models of uncertainty into a single resultant model. Many existing approaches to fusion use subjective quantities such as 'strengths of belief' and process these…
This paper presents a Hoare-style calculus for formal reasoning about reconfiguration programs of distributed systems. Such programs create and delete components and/or interactions (connectors) while the system components change state…
While Chain-of-Thought (CoT) prompting enhances the reasoning capabilities of large language models, the faithfulness of the generated rationales remains an open problem for model interpretability. We propose a novel theoretical lens for…
This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization…
In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of…
Program slicing has been mainly studied in the context of imperative languages, where it has been applied to a wide variety of software engineering tasks, like program understanding, maintenance, debugging, testing, code reuse, etc. This…
Using arbitrary symplectic structures and parametrization invariant actions, we develop a formalism, based on Dirac's quantization procedure, that allows us to consider theories with both space-space as well as space-time noncommutativity.…
The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…
Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
We study counting propositional logic as an extension of propositional logic with counting quantifiers. We prove that the complexity of the underlying decision problem perfectly matches the appropriate level of Wagner's counting hierarchy,…
Taha and Nielsen have developed a multi-stage calculus {\lambda}{\alpha} with a sound type system using the notion of environment classifiers. They are special identifiers, with which code fragments and variable declarations are annotated,…