相关论文: Higher-Order Termination: from Kruskal to Computab…

Dirac notation is widely used in quantum physics and quantum programming languages to define, compute and reason about quantum states. This paper considers Dirac notation from the perspective of automated reasoning. We prove two main…

We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…

A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…

Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…

We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded…

We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…

One of the long-standing problems on logic programming is to express {\it priority}-related operations -- default reasoning, if-then-else, cut, exception handling, etc -- in a high-level way. We argue that this problem can be solved by…

Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…

This paper proposes a type-and-effect system called Teqt, which distinguishes terminating terms and total functions from possibly diverging terms and partial functions, for a lambda calculus with general recursion and equality types. The…

Large Reasoning Models (LRMs) achieve impressive performance on complex reasoning tasks via Chain-of-Thought (CoT) reasoning, which enables them to generate intermediate thinking tokens before arriving at the final answer. However, LRMs…

The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…

The semantics of the Prolog ``cut'' construct is explored in the context of some desirable properties of logic programming systems, referred to as the witness properties. The witness properties concern the operational consistency of…

Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…

The semantic foundations for logic programming are usually separated into two different approaches. The operational semantics, which uses SLD-resolution, the proof method that computes answers in logic programming, and the declarative…

The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…

This paper considers the computational hardness of computing expected outcomes and deciding almost-sure termination of probabilistic programs. We show that deciding almost-sure termination and deciding whether the expected outcome of a…

Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…

Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…

In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…

We propose an early termination technique for mixed integer conic programming for use within branch-and-bound based solvers. Our approach generalizes previous early termination results for ADMM-based solvers to a broader class of…