Related papers: Generic Automatic Proof Tools
Recent advances in automated theorem proving leverages language models to explore expanded search spaces by step-by-step proof generation. However, such approaches are usually based on short-sighted heuristics (e.g., log probability or…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
Proof by induction plays a central role in formal verification. However, its automation remains as a formidable challenge in Computer Science. To solve inductive problems, human engineers often have to provide auxiliary lemmas manually. We…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and…
This dialog paper offers a preview and provides a foretaste of an upcoming work on the axiomatization of basic interactive algorithms. The modern notion of algorithm was elucidated in the 1930s--1950s. It was axiomatized a quarter of a…
Classical first-order logic is in many ways central to work in mathematics, linguistics, computer science and artificial intelligence, so it is worthwhile to define it in full detail. We present soundness and completeness proofs of a…
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…
Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…
There is a long tradition of fruitful interaction between logic and social choice theory. In recent years, much of this interaction has focused on computer-aided methods such as SAT solving and interactive theorem proving. In this paper, we…
We introduce pseudo-deterministic interactive proofs (psdAM): interactive proof systems for search problems where the verifier is guaranteed with high probability to output the same output on different executions. As in the case with…
This paper presents meta-logical investigations based on category theory using the proof assistant Isabelle/HOL. We demonstrate the potential of a free logic based shallow semantic embedding of category theory by providing a formalization…
We provide simple equational principles for deriving rely-guarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution…
Algebraic effects and handlers are a powerful abstraction to build non-local control-flow mechanisms such as resumable exceptions, lightweight threads, co-routines, generators, and asynchronous I/O. All of such features have very evolved…
We present Cobra, a modern proof presentation framework, leveraging cutting-edge presentation technology together with a state of the art interactive theorem prover to present formalized mathematics as active documents. Cobra provides both…
A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other…
We give a method to transform into programs, classical proofs using a well ordering of the reals. The technics uses a generalization of Cohen's forcing and the theory of classical realizability introduced by the author.
Church's thesis claims that all effecticely calculable functions are recursive. A shortcoming of the various definitions of recursive functions lies in the fact that it is not a matter of a syntactical check to find out if an entity gives…