相关论文: Ground Canonicity
This paper attempts to address the question of how best to assure the correctness of saturation-based automated theorem provers using our experience developing the theorem prover Vampire. We describe the techniques we currently employ to…
We analyze possibilities of second-order quantifier elimination for formulae containing parameters -- constants or functions. For this, we use a constraint resolution calculus obtained from specializing the hierarchical superposition…
We carry out a proof theoretic analysis of the wellfoundedness of recursive path orders in an abstract setting. We outline a very general termination principle and extract from its wellfoundedness proof subrecursive bounds on the size of…
In this paper we investigate the Curry-Howard correspondence for constructive modal logic in light of the gap between the proof equivalences enforced by the lambda calculi from the literature and by the recently defined winning strategies…
The inverse method is a saturation based theorem proving technique; it relies on a forward proof-search strategy and can be applied to cut-free calculi enjoying the subformula property. Here we apply this method to derive the unprovability…
The interplay between the two fundamental concepts of topological order and reflection positivity allows one to characterize the ground states of certain many-body Hamiltonians. We define topological order in an appropriate fashion and show…
This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case study of definitions of randomness in…
Equality saturation is an emerging technique for program and query optimization developed in the programming language community. It performs term rewriting over an E-graph, a data structure that compactly represents a program space. Despite…
We explore the idea of using automatic and similar kind of presentations of structures to deal with the conceptual problem of natural proof-theoretic ordinal notations. We conclude that this approach still does not meet the goals.
We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…
Existing works have studied the impacts of the order of words within natural text. They usually analyze it by destroying the original order of words to create a scrambled sequence, and then comparing the models' performance between the…
We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give…
This talk is an attempt to review all our knowledge on saturation at low $x$ both theoretical and experimental, to stimulate a search for saturation effects at THERA. The main goals of this presentation are 1. To discuss an intuitive…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…
Some general properties of abstract relations are closely examined. These include generalizations of linearity, and properties based on `pinning' an inequality by a pair of families of endomorphisms.To each property we try to associate a…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
We explore the enumeration of some natural classes of graded posets, including all graded posets, (2+2)- and (3+1)-avoiding graded posets, (2+2)-avoiding graded posets, and (3+1)-avoiding graded posets. We obtain enumerative and structural…
While rule-based attribution methods have proven useful for providing local explanations for Deep Neural Networks, explaining modern and more varied network architectures yields new challenges in generating trustworthy explanations, since…