Related papers: A First-Order Logic with Frames
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…
In this paper we propose a logic-based, framework inspired by artificial intelligence, but scaled down for practical database and programming applications. Computation in the framework is viewed as the task of generating a sequence of state…
We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…
First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information. In this paper, a particular first-order learning system is modified to customize it for finding…
A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed…
Many classical planning frameworks are built on first-order languages. The first-order expressive power is desirable for compactly representing actions via schemas, and for specifying quantified conditions such as $\neg\exists…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
We consider the family of guarded and unguarded ordered logics, that constitute a recently rediscovered family of decidable fragments of first-order logic (FO), in which the order of quantification of variables coincides with the order in…
Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…
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…
We introduce a proper display calculus for first-order logic, of which we prove soundness, completeness, conservativity, subformula property and cut elimination via a Belnap-style metatheorem. All inference rules are closed under uniform…
We consider a simple extension of logic programming where variables may range over goals and goals may be arguments of predicates. In this language we can write logic programs which use goals as data. We give practical evidence that, by…
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…
We investigate the properties of Inclusion Logic, that is, First Order Logic with Team Semantics extended with inclusion dependencies. We prove that Inclusion Logic is equivalent to Greatest Fixed Point Logic, and we prove that all…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…
To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on procedural questions. This would enable an account of…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…