相关论文: Deciding Predicate Logical Theories of Real-Valued…

We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…

We describe and compare design choices for meta-predicate semantics, as found in representative Prolog module systems and in Logtalk. We look at the consequences of these design choices from a pragmatic perspective, discussing explicit…

Let V be a set of number-theoretical functions. We define a notion of absolute V-realizability for predicate formulas and sequents in such a way that the indices of functions in V are used for interpreting the implication and the universal…

Real world programming languages crucially depend on the availability of computational effects to achieve programming convenience and expressive power as well as program efficiency. Logical frameworks rely on predicates, or dependent types,…

Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…

A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…

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 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…

We present a declarative language, PP, for the high-level specification of preferences between possible solutions (or trajectories) of a planning problem. This novel language allows users to elegantly express non-trivial, multi-dimensional…

Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…

Representing time is crucial for cyber-physical systems and has been studied extensively in the Situation Calculus. The most commonly used approach represents time by adding a real-valued fluent $\mathit{time}(a)$ that attaches a time point…

We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and…

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…

This paper describes and motivates a new decision theory known as functional decision theory (FDT), as distinct from causal decision theory and evidential decision theory. Functional decision theorists hold that the normative principle for…

We analyze the problem of defining well-founded semantics for ordered logic programs within a general framework based on alternating fixpoint theory. We start by showing that generalizations of existing answer set approaches to preference…

Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…

While modal extensions of decidable fragments of first-order logic are usually undecidable, their monodic counterparts, in which formulas in the scope of modal operators have at most one free variable, are typically decidable. This only…

We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…

We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under 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…