Related papers: From First-Order Logic to Assertional Logic

In this paper we considered the extension of the First-order Logic (FOL) by Bealer's intensional abstraction operator. Contemporary use of the term 'intension' derives from the traditional logical Frege-Russell's doctrine that an idea…

We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…

Inclusion logic is a variant of dependence logic that was shown to have the same expressive power as positive greatest fixed-point logic. Inclusion logic is not axiomatizable in full, but its first-order consequences can be axiomatized. In…

AGI (Strong AI) aims to create intelligent robots that are quasi indistinguishable from the human mind. Like a child, the AGI robot would have to learn through input and experiences, constantly progressing and advancing its abilities over…

This paper continues the discussion of the representation of ontologies in the first-order logical environment FOLE. According to Gruber, an ontology defines the primitives with which to model the knowledge resources for a community of…

Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…

We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…

We introduce a logic for reasoning about evidence, that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…

There has been a longstanding dispute over which formalism is the best for representing knowledge in AI. The well-known "declarative vs. procedural controversy" is concerned with the choice of utilizing declarations or procedures as the…

Previous research into the relation between ASP and classical logic has identified at least two different ways in which the former extends the latter. First, ASP program typically contain sets of rules that can be naturally interpreted as…

Artificial Intelligence aims to provide computer programs with commonsense knowledge to reason about our world. This paper offers a new practical approach towards automated commonsense reasoning with first-order logic (FOL) ontologies. We…

We introduce a natural Turing-complete extension of first-order logic FO. The extension adds two novel features to FO. The first one of these is the capacity to add new points to models and new tuples to relations. The second one is the…

We present a mechanism for constructing graphical models, specifically Bayesian networks, from a knowledge base of general probabilistic information. The unique feature of our approach is that it uses a powerful first-order probabilistic…

Modular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We…

We introduce the first order logic of proofs $FOLP^\Box$ in the joint language combining justification terms and binding modalities. The main issue is Kripke--style semantics for this logic. We describe models for $FOLP^\Box$ in terms of…

First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type…

Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…

We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…

Most non-classical logics are subclassical, that is, every inference/theorem they validate is also valid classically. A notable exception is the three-valued propositional Logic of Ordinary Discourse (OL) proposed and extensively motivated…

Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon…