相关论文: Escape to Mizar for ATPs
A considerable body of work in AI has been concerned with aggregating measures of confirmatory and disconfirmatory evidence for a common set of propositions. Claiming classical probability to be inadequate or inappropriate, several…
In this work, we prove over 3000 previously ATP-unproved Mizar/MPTP problems by using several ATP and AI methods, raising the number of ATP-solved Mizar problems from 75\% to above 80\%. First, we start to experiment with the cvc5 SMT…
Inventing targeted proof search strategies for specific problem sets is a difficult task. State-of-the-art automated theorem provers (ATPs) such as E allow a large number of user-specified proof search strategies described in a rich domain…
We present a tool that automates termination proofs for recursive definitions by mining existing termination theorems.
We introduce a novel task consisting in assigning a proof to a given mathematical statement. The task is designed to improve the processing of research-level mathematical texts. Applying Natural Language Processing (NLP) tools to research…
Linearizability is a standard correctness criterion for concurrent algorithms, typically proved by establishing the algorithms' linearization points. However, relying on linearization points leads to proofs that are…
Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly…
Rationalization empowers deep learning models with self-explaining capabilities through a cooperative game, where a generator selects a semantically consistent subset of the input as a rationale, and a subsequent predictor makes predictions…
The On-Line Encyclopedia Of Integer Sequences , that wonderful resource that most combinatorialists, and many other mathematicians and scientists, use at least once a day, is a treasure trove of mathematical information, and, one of its…
We give a complete classification of the set of parameters $\kappa$ for which the singular value of $E_{\kappa}:z\mapsto \exp(z)+\kappa$ escapes to infinity under iteration. In particular, we show that every path-connected component of this…
The ability to automatically generalise (interactive) proofs and use such generalisations to discharge related conjectures is a very hard problem which remains unsolved. Here, we develop a notion of goal types to capture key properties of…
The modularity theorem implies that for every elliptic curve $E /\mathbb{Q}$ there exist rational maps from the modular curve $X_0(N)$ to $E$, where $N$ is the conductor of $E$. These maps may be expressed in terms of pairs of modular…
Translating expressions between different logics and theorem provers is notoriously and often prohibitively difficult, due to the large differences between the logical foundations, the implementations of the systems, and the structure of…
Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly…
Automated theorem provers (ATPs) can disprove conjectures by saturating a set of clauses, but the resulting saturated sets are opaque certificates. In the unit equational fragment, a saturated set can in fact be read as a convergent rewrite…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
One of the most annoying aspects in the formalization of mathematics is the need of transforming notions to match a given, existing result. This kind of transformations, often based on a conspicuous background knowledge in the given…
This paper introduces a propositional encoding for lexicographic path orders in connection with dependency pairs. This facilitates the application of SAT solvers for termination analysis of term rewrite systems based on the dependency pair…
Nondeterminism in scheduling is the cardinal reason for difficulty in proving correctness of concurrent programs. A powerful proof strategy was recently proposed [6] to show the correctness of such programs. The approach captured data-flow…