Related papers: Open Higher-Order Logic (Long Version)
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is…
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…
We generalize Kracht's theory of internal describability from classical modal logic to the family of all logics canonically associated with varieties of normal lattice expansions (LE algebras). We work in the purely algebraic setting of…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…
Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…
In flowchart languages, predicates play an interesting double role. In the textual representation, they are often presented as conditions, i.e., expressions which are easily combined with other conditions (often via Boolean combinators) to…
In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
We introduce APPL (Abstract Program Property Logic), a unifying Hoare-style logic that subsumes standard Hoare logic, incorrectness logic, and several variants of Hyper Hoare logic. APPL provides a principled foundation for abstract program…
Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…
Local-order-invariant (first-order) logic is an extension of first-order logic where formulae have access to a ternary local order relation on the Gaifman graph, provided that the truth value does not depend on the specific order relation…
This paper aims to provide an analysis of what it means when we say that a pair of theories, very generously construed, are equivalent in the sense that they are interdefinable. With regard to theories articulated in first order logic, we…
An attempt at unifying logic and functional programming is reported. As a starting point, we take the view that "logic programs" are not about logic but constitute inductive definitions of sets and relations. A skeletal language design…
We study possibilities for algebraic closures, differences between definable and algebraic closures in first-order structures, and variations of these closures with respect to the bounds of cardinalities of definable sets and given sets of…
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…
First-order logic is known to have limited expressive power over finite structures. It enjoys in particular the locality property, which states that first-order formulae cannot have a global view of a structure. This limitation ensures on…
If $\mathcal{L}$ is an abstract logic (a.k.a. model theoretic logic), we can define the inner model $C(\mathcal{L})$ by replacing first order logic with $\mathcal{L}$ in G\"odel's definition of the inner model $L$ of constructible sets. Set…