Related papers: Outcome Logic: A Unifying Foundation for Correctne…

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…

Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…

We describe the integration of logical and uncertain reasoning methods to identify the likely source and location of software problems. To date, software engineers have had few tools for identifying the sources of error in complex software…

Satisfiability-based automated reasoning is an approach that is being successfully used in software engineering to validate complex software, including for safety-critical systems. Such reasoning underlies many validation activities, from…

Automated verification of all members of a (potentially infinite) set of programs has the potential to be useful in program synthesis, as well as in verification of dynamically loaded code, concurrent code, and language properties. Existing…

Programs increasingly rely on randomization in applications such as cryptography and machine learning. Analyzing randomized programs has been a fruitful research direction, but there is a gap when programs also exploit nondeterminism (for…

Because contemporary large software systems are pervasively inconsistent, it is not safe to reason about them using classical logic. The goal of Direct Logic is to be a minimal fix to classical mathematical logic that meets the requirements…

Dynamic logic is a powerful approach to reasoning about programs and their executions, obtained by extending classical logic with modalities that can express program executions as formulas. However, the use of dynamic logic in the setting…

The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…

If two experts disagree on a test, we may conclude both cannot be 100 per cent correct. But if they completely agree, no possible evaluation can be excluded. This asymmetry in the utility of agreements versus disagreements is explored here…

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…

Computability logic (CoL) is a formal theory of interactive computation. It understands computational problems as games played by two players: a machine and its environment, uses logical formalism to describe valid principles of…

Verifying a real-world program's functional correctness can be decomposed into (1) a refinement proof showing that the program implements a more abstract high-level program and (2) an algorithm correctness proof at the high level.…

Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms, and recent years have seen a number of proposals of program logics for proving it. Although these logics differ in technical details, they…

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…

In the 1980s a new, extraordinarily productive way of reasoning about algorithms emerged. In this paper, we introduce the term "outcome reasoning" to refer to this form of reasoning. Though outcome reasoning has come to dominate areas of…

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…

Abstract interpretation, Hoare logic, and incorrectness (or reverse Hoare) logic are powerful techniques for static analysis of computer programs. All of them have been successfully extended to the quantum setting, but largely developed in…

Negation as failure and incomplete information in logic programs have been studied by many researchers In order to explains HOW a negated conclusion was reached, we introduce and proof a different way for negating facts to overcoming…

Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates…