Related papers: Semantics for first-order superposition logic
Suppose we want to build a system that answers a natural language question by representing its semantics as a logical form and computing the answer given a structured database of facts. The core part of such a system is the semantic parser…
This paper discusses the representation of ontologies in the first-order logical environment {\ttfamily FOLE}. An ontology defines the primitives with which to model the knowledge resources for a community of discourse. These primitives…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
In this paper we adapt the definitions and results from Apt and Vermeulen on `First order logic as a constraint programming language' (in: Proceedings of LPAR2001, Baaz and Voronkov (eds.), Springer LNAI 2514) to include important ideas…
The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. Such logic formally extends logic programming, abductive logic programming and datalog, and thus formalizes…
In Probabilistic Logic Nilsson uses the device of a probability distribution over a set of possible worlds to assign probabilities to the sentences of a logical language. In his paper Nilsson concentrated on inference and associated…
We develop a system for solving logical deduction one-dimensional ordering problems by transforming natural language premises and candidate statements into first-order logic. Building on Heim and Kratzer's syntax-based compositional…
We introduce an extension of the propositional calculus to include abstracts of predicates and quantifiers, employing a single rule along with a novel comprehension schema and a principle of extensionality, which are substituted for the…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
We address the problem of semantic querying of relational databases (RDB) modulo knowledge bases using very expressive knowledge representation formalisms, such as full first-order logic or its various fragments. We propose to use a…
At the core of the quest for a logic for PTime is a mismatch between algorithms making arbitrary choices and isomorphism-invariant logics. One approach to overcome this problem is witnessed symmetric choice. It allows for choices from…
We present three syntactic forcing models for coherent logic. These are based on sites whose underlying category only depends on the signature of the coherent theory, and they do not presuppose that the logic has equality. As an application…
We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is a FO-definable language that is monotone in monadic predicates but not definable in FO+. This provides…
A policy describes the conditions under which an action is permitted or forbidden. We show that a fragment of (multi-sorted) first-order logic can be used to represent and reason about policies. Because we use first-order logic, policies…
We investigate an operator on classes of languages. For each class $C$, it outputs a new class $FO^2(I_C)$ associated with a variant of two-variable first-order logic equipped with a signature$I_C$ built from $C$. For $C = \{\emptyset,…
Modal logic with propositional quantifiers (i.e. second-order propositional modal logic (SOPML)) has been considered since the early time of modal logic. Its expressive power and complexity are high, and its van-Benthem-Rosen theorem and…
Model checking linear-time properties expressed in first-order logic has non-elementary complexity, and thus various restricted logical languages are employed. In this paper we consider two such restricted specification logics, linear…
The importance of taking individual, potentially conflicting perspectives into account when dealing with knowledge has been widely recognised. Many existing ontology management approaches fully merge knowledge perspectives, which may…
We compare three satisfiability notions for propositional formulas in the language {not, and, or} over a fixed finite-dimensional Hilbert space H=F^d with F in {R, C}. The first is the standard Hilbert-lattice semantics on the subspace…