Related papers: Clause Set Cycles and Induction
CZF is a system of set theory which, over classical logic, is equivalent to ZF, while over intuitionistic logic, it has a well-known constructive type-theoretic interpretation. This article introduces a simpler, intuitive family of…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…
These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…
Whitney's broken circuit theorem gives a graphical example to reduce the number of the terms in the sum of the inclusion-exclusion formula by a predicted cancellation. So far, the known cancellations for the formula strongly depend on the…
We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.
The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a…
Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…
Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…
Well-known principles of induction include monotone induction and different sorts of non-monotone induction such as inflationary induction, induction over well-founded sets and iterated induction. In this work, we define a logic formalizing…
We propose analyzing conditional reasoning by appeal to a notion of intervention on a simulation program, formalizing and subsuming a number of approaches to conditional thinking in the recent AI literature. Our main results include a…
Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus…
We present a~novel approach to the problem of automated theorem proving. Polynomial cost procedures that recognise sentences belonging to a theory are generated on a basis of a set of axioms of the so-called Truncated Predicate Calculus…
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…