Related papers: Induction and Skolemization in saturation theorem …
We study variants of Buss's theories of bounded arithmetic axiomatized by induction schemes disallowing the use of parameters, and closely related induction inference rules. We put particular emphasis on $\hat\Pi^b_i$ induction schemes,…
In this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…
We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…
A 0-1 matrix $M$ contains a 0-1 matrix pattern $P$ if we can obtain $P$ from $M$ by deleting rows and/or columns and turning arbitrary 1-entries into 0s. The saturation function $\mathrm{sat}(P,n)$ for a 0-1 matrix pattern $P$ indicates the…
When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…
In this work, we propose a new method to integrate two recent lines of work: unsupervised induction of shallow semantics (e.g., semantic roles) and factorization of relations in text and knowledge bases. Our model consists of two…
We develop a framework for model checking infinite-state systems by automatically augmenting them with auxiliary variables, enabling quantifier-free induction proofs for systems that would otherwise require quantified invariants. We combine…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
We generalize the notion of proof term to the realm of transfinite reduction. Proof terms represent reductions in the first-order term format, thereby facilitating their formal analysis. We show that any transfinite reduction can be…
An inductive proof can be represented as a proof schema, i.e. as a parameterized sequence of proofs defined in a primitive recursive way. A corresponding cut-elimination method, called schematic CERES, can be used to analyze these proofs,…
We propose a local model-checking proof system for a fragment of CTL. The rules of the proof system are motivated by the well-known fixed-point characterisation of CTL based on unfolding of the temporal operators. To guarantee termination…
We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…
Robotic cell injection is used for automatically delivering substances into a cell and is an integral component of drug development, genetic engineering and many other areas of cell biology. Traditionally, the correctness of functionality…
Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
G\"odel's Incompleteness Theorems suggest that no single formal system can capture the entirety of one's mathematical beliefs, while pointing at a hierarchy of systems of increasing logical strength that make progressively more explicit…
We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…
We prove an asymptotic saturation-type version of Rota's basis conjecture. It relies on the connection of Tao's slice rank with unstable tensors from geometric invariant theory.
We suggest that the correspondence between gauge theories strongly coupled in the infrared and their low energy effective theories may be probed by introducing topologically non-trivial background scalar fields. We argue that one loop…
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…