A Multi-agent approach to first-order logic

1997 ◽  
pp. 167-178 ◽  
Author(s):  
Guilherme Bittencourt ◽  
Isabel Tonin
Keyword(s):  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Multi Agent

scholarly journals Satisfiability in Strategy Logic Can Be Easier than Model Checking

2019 ◽  
Vol 33 ◽  
pp. 2638-2645 ◽  
Author(s):  
Erman Acar ◽  
Massimo Benerecetti ◽  
Fabio Mogavero
Keyword(s):  
Model Checking ◽  
Order Logic ◽  
First Order Logic ◽  
Multi Agent Systems ◽  
First Order ◽  
Systems Model ◽  
Multi Agent ◽  
Decidable Fragment ◽  
Game Theoretic ◽  
Strategy Logic

In the design of complex systems, model-checking and satisfiability arise as two prominent decision problems. While model-checking requires the designed system to be provided in advance, satisfiability allows to check if such a system even exists. With very few exceptions, the second problem turns out to be harder than the first one from a complexity-theoretic standpoint. In this paper, we investigate the connection between the two problems for a non-trivial fragment of Strategy Logic (SL, for short). SL extends LTL with first-order quantifications over strategies, thus allowing to explicitly reason about the strategic abilities of agents in a multi-agent system. Satisfiability for the full logic is known to be highly undecidable, while model-checking is non-elementary.The SL fragment we consider is obtained by preventing strategic quantifications within the scope of temporal operators. The resulting logic is quite powerful, still allowing to express important game-theoretic properties of multi-agent systems, such as existence of Nash and immune equilibria, as well as to formalize the rational synthesis problem. We show that satisfiability for such a fragment is PSPACE-COMPLETE, while its model-checking complexity is 2EXPTIME-HARD. The result is obtained by means of an elegant encoding of the problem into the satisfiability of conjunctive-binding first-order logic, a recently discovered decidable fragment of first-order logic.

scholarly journals Interactions between Knowledge and Time in a First-Order Logic for Multi-Agent Systems: Completeness Results

2012 ◽  
Vol 45 ◽  
pp. 1-45 ◽  
Author(s):  
F. Belardinelli ◽  
A. Lomuscio
Keyword(s):  
Epistemic Logic ◽  
Order Logic ◽  
First Order Logic ◽  
Multi Agent Systems ◽  
Perfect Recall ◽  
Initial State ◽  
Agent Systems ◽  
First Order ◽  
Multi Agent ◽  
Order Extension

We investigate a class of first-order temporal-epistemic logics for reasoning about multi-agent systems. We encode typical properties of systems including perfect recall, synchronicity, no learning, and having a unique initial state in terms of variants of quantified interpreted systems, a first-order extension of interpreted systems. We identify several monodic fragments of first-order temporal-epistemic logic and show their completeness with respect to their corresponding classes of quantified interpreted systems.

A Multi-Agent Scheme for Real-Time Fact Mapping of Reasoning Engine

2014 ◽  
Vol 563 ◽  
pp. 172-176
Author(s):  
You Miao Qu ◽  
Wei Hua Li ◽  
Hua Sheng Chen
Keyword(s):  
Real Time ◽  
Physical World ◽  
Order Logic ◽  
First Order Logic ◽  
System Delay ◽  
Agent Based ◽  
Mapping Algorithm ◽  
First Order ◽  
Multi Agent ◽  
Reasoning Engine

Physical world facts must be measured and translated into first-order-logic expression before participate the reasoning process in reasoning engine. However, mapping facts into first-order-logic form in real-time is not an easy task. This paper discusses the difficulties of such mapping in three aspects. Then, this paper proposes a multi-agent based scheme to solve these three problems. First, this paper introduces multi-agent frame to reduce system design complexity. Then, this paper proposes a table mapping algorithm to translate numeric facts into first-order-logic form. After that, a resampling mechanism considering overall system delay is introduced to selectively remove excessive facts. Finally, this paper gives a case study, which verifies that the scheme proposed in this paper is practical, efficient and easy to put into application.

First-Order Logic Reasoning Support for the Semantic Web

2009 ◽  
Vol 19 (12) ◽  
pp. 3091-3099 ◽  
Author(s):  
Gui-Hong XU ◽  
Jian ZHANG
Keyword(s):  
Semantic Web ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Logic Reasoning

Boolean-valued structures

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Model Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Rules ◽  
Mathematical Concepts ◽  
Semantic Framework ◽  
First Order ◽  
Standard Models ◽  
Boolean Valued Model ◽  
Semantic Values

Chapters 6-12 are driven by questions about the ability to pin down mathematical entities and to articulate mathematical concepts. This chapter is driven by similar questions about the ability to pin down the semantic frameworks of language. It transpires that there are not just non-standard models, but non-standard ways of doing model theory itself. In more detail: whilst we normally outline a two-valued semantics which makes sentences True or False in a model, the inference rules for first-order logic are compatible with a four-valued semantics; or a semantics with countably many values; or what-have-you. The appropriate level of generality here is that of a Boolean-valued model, which we introduce. And the plurality of possible semantic values gives rise to perhaps the ‘deepest’ level of indeterminacy questions: How can humans pin down the semantic framework for their languages? We consider three different ways for inferentialists to respond to this question.

scholarly journals GAMES AND CARDINALITIES IN INQUISITIVE FIRST-ORDER LOGIC

2021 ◽  
pp. 1-28
Author(s):  
IVANO CIARDELLI ◽  
GIANLUCA GRILLETTI
Keyword(s):  
Order Logic ◽  
First Order Logic ◽  
First Order

scholarly journals Extensions in graph normal form

2020 ◽  
Author(s):  
Michał Walicki
Keyword(s):  
Normal Form ◽  
Fixed Points ◽  
Propositional Logic ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Special Cases

Abstract Graph normal form, introduced earlier for propositional logic, is shown to be a normal form also for first-order logic. It allows to view syntax of theories as digraphs, while their semantics as kernels of these digraphs. Graphs are particularly well suited for studying circularity, and we provide some general means for verifying that circular or apparently circular extensions are conservative. Traditional syntactic means of ensuring conservativity, like definitional extensions or positive occurrences guaranteeing exsitence of fixed points, emerge as special cases.

Relational Chase Procedures Interpreted as Resolution with Paramodulation1

1991 ◽  
Vol 15 (2) ◽  
pp. 123-138
Author(s):  
Joachim Biskup ◽  
Bernhard Convent
Keyword(s):  
Alternative Interpretation ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Problem ◽  
First Order ◽  
Inference Problems ◽  
The One ◽  
The Relationship ◽  
Theoretical Foundations ◽  
Insight Into

In this paper the relationship between dependency theory and first-order logic is explored in order to show how relational chase procedures (i.e., algorithms to decide inference problems for dependencies) can be interpreted as clever implementations of well known refutation procedures of first-order logic with resolution and paramodulation. On the one hand this alternative interpretation provides a deeper insight into the theoretical foundations of chase procedures, whereas on the other hand it makes available an already well established theory with a great amount of known results and techniques to be used for further investigations of the inference problem for dependencies. Our presentation is a detailed and careful elaboration of an idea formerly outlined by Grant and Jacobs which up to now seems to be disregarded by the database community although it definitely deserves more attention.

scholarly journals Formula size games for modal logic and μ-calculus

2019 ◽  
Vol 29 (8) ◽  
pp. 1311-1344 ◽  
Author(s):  
Lauri T Hella ◽  
Miikka S Vilander
Keyword(s):  
Modal Logic ◽  
Optimal Strategy ◽  
Order Logic ◽  
First Order Logic ◽  
Kripke Models ◽  
First Order ◽  
Modal Operators ◽  
Crucial Difference ◽  
Definition Of ◽  
Person Game

Abstract We propose a new version of formula size game for modal logic. The game characterizes the equivalence of pointed Kripke models up to formulas of given numbers of modal operators and binary connectives. Our game is similar to the well-known Adler–Immerman game. However, due to a crucial difference in the definition of positions of the game, its winning condition is simpler, and the second player does not have a trivial optimal strategy. Thus, unlike the Adler–Immerman game, our game is a genuine two-person game. We illustrate the use of the game by proving a non-elementary succinctness gap between bisimulation invariant first-order logic $\textrm{FO}$ and (basic) modal logic $\textrm{ML}$. We also present a version of the game for the modal $\mu $-calculus $\textrm{L}_\mu $ and show that $\textrm{FO}$ is also non-elementarily more succinct than $\textrm{L}_\mu $.

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