Related papers: Tableaux Modulo Theories Using Superdeduction
Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice. Reasoning with primitive equality is enabled by adapting paramodulation-based proof search to higher-order logic. The prover may cooperate…
We describe a method for predicting a classification of an object given classifications of the objects in the training set, assuming that the pairs object/classification are generated by an i.i.d. process from a continuous probability…
Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…
The design of embedded systems, that are ubiquitously used in mobile devices and cars, is becoming continuously more complex such that efficient system-level design methods are becoming crucial. My research aims at developing systems that…
This work explores the application of deep learning, a machine learning technique that uses deep neural networks (DNN) in its core, to an automated theorem proving (ATP) problem. To this end, we construct a statistical model which…
Semi-algebraic proof systems such as sum-of-squares (SoS) have attracted a lot of attention recently due to their relation to approximation algorithms: constant degree semi-algebraic proofs lead to conjecturally optimal polynomial-time…
Taxonomies are an important ingredient of knowledge organization, and serve as a backbone for more sophisticated knowledge representations in intelligent systems, such as formal ontologies. However, building taxonomies manually is a costly…
We present the results from Meno, a simple autoformalizer that proves theorems in Lean by systematically exploring the space of both formal and informal proofs, and tactic ablation, a new method for exploring mathematical creativity under…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
We present SGDPLL(T), an algorithm that solves (among many other problems) probabilistic inference modulo theories, that is, inference problems over probabilistic models defined via a logic theory provided as a parameter (currently,…
Following the types-as-sets paradigm, we present a mechanized embedding of dependent function types with a hierarchy of universes into schematic first-order logic with equality, with axiom schemas of Tarski-Grothendieck set theory. We carry…
We scale layered modal type theory to dependent types, introducing DeLaM, dependent layered modal type theory. This type theory is novel in that we have one uniform type theory in which we can not only compose and execute code, but also…
Classically, in saturation-based proof systems, unification has been considered atomic. However, it is also possible to move unification to the calculus level, turning the steps of the unification algorithm into inferences. For calculi that…
In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…
Previous formulations of group theory in ACL2 and Nqthm, based on either "encapsulate" or "defn-sk", have been limited by their failure to provide a path to proof by induction on the order of a group, which is required for most interesting…
The introduction of automated deduction systems in secondary schools face several bottlenecks. Beyond the problems related with the curricula and the teachers, the dissonance between the outcomes of the geometry automated theorem provers…
This thesis provides methods and analysis of models which make progress on this goal. The techniques outlined are task agnostic, and should provide benefit when used with nearly any transformer LM. We introduce two new finetuning methods…
Module extraction - the task of computing a (preferably small) fragment M of an ontology T that preserves entailments over a signature S - has found many applications in recent years. Extracting modules of minimal size is, however,…
We introduce a new Gentzen-style framework of grafted hypersequents that combines the formalism of nested sequents with that of hypersequents. To illustrate the potential of the framework, we present novel calculi for the modal logics…