Related papers: Induction Models on \mathbb{N}
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
The unification algorithm has long been a target for program synthesis research, but a fully automatic derivation remains a research goal. In deductive program synthesis, computer programming is phrased as a task in theorem proving; a…
We construct Quantum Representation Theory which describes quantum analogue of representations in frame of "non-commutative linear geometry" developed by Manin. To do it we generalise the internal hom-functor to the case of adjunction with…
Higher inductive types are a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style. They have proven very fruitful for the "synthetic" development of homotopy…
Can a physicist make only a finite number of errors in the eternal quest to uncover the law of nature? This millennium-old philosophical problem, known as inductive inference, lies at the heart of epistemology. Despite its significance to…
We introduce a new form of SAT-based symbolic model checking. One common idea in SAT-based symbolic model checking is to generate new clauses from states that can lead to property violations. Our previous work suggests applying induction to…
We give an algebraic characterization of the syntax and operational semantics of a class of simply-typed languages, such as the language PCF: we characterize simply-typed syntax with variable binding and equipped with reduction rules via a…
Conducting contamination-free evaluation of mathematical capabilities can be difficult for two reasons: models may memorize a test set once it is made public, and current mathematical benchmarks are prone to overfitting due to having…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
Embedding models, which learn latent representations of users and items based on user-item interaction patterns, are a key component of recommendation systems. In many applications, contextual constraints need to be applied to refine…
The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical…
Rewriting Induction (RI) is a method to prove inductive theorems, originating from equational reasoning. By using Logically Constrained Simply-typed Term Rewriting Systems (LCSTRSs) as an intermediate language, rewriting induction becomes a…
The authors are doing the readers of Statistical Science a true service with a well-written and up-to-date overview of boosting that originated with the seminal algorithms of Freund and Schapire. Equally, we are grateful for high-level…
Rewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages,…
In order to enable model-based, iterative design of safety-relevant systems, an efficient incorporation of safety and system engineering is a pressing need. Our approach interconnects system design and safety analysis models efficiently…
We present a base class of automata that induce a numeration system and we give an algorithm to give the n-th word in the language of the automaton when the expansion of n in the induced numeration system is feeded to the automaton.…
This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined…
Just as the $\lambda$-calculus uses three primitives (abstraction, application, variable) as the foundation of functional programming, inheritance-calculus uses three primitives (record, definition, inheritance) as the foundation of…
Inductive Logic Programming (ILP) learns interpretable logical rules from data. Existing methods are transductive: their learned parameters are bound to specific predicates and require retraining for each new task. We introduce Neural Rule…
Theory revision integrates inductive learning and background knowledge by combining training examples with a coarse domain theory to produce a more accurate theory. There are two challenges that theory revision and other theory-guided…