An epistemic model of an agent who does not reflect on reasoning processes

This paper introduces an epistemic model of a boundedly rational agent under the two assumptions that (i) the agent’s reasoning process is in accordance with the model but (ii) the agent does not reflect on these reasoning processes. For such a concept of bounded rationality a semantic interpretation by the possible world semantics of the Kripke (1963) type is no longer available because the definition of knowledge in these possible world semantics implies that the agent knows all valid statements of the model. The key to my alternative semantic approach is the extension of the method of truth tables, first introduced for the propositional logic by Wittgenstein (1922), to an epistemic logic so that I can determine the truth value of epistemic statements for all relevant truth conditions. In my syntactic approach I define an epistemic logic–consisting of the classical calculus of propositional logic plus two knowledge axioms–that does not include the inference rule of necessitation, which claims that an agent knows all theorems of the logic. As my main formal result I derive a determination theorem linking my semantic with my syntactic approach. The difference between my approach and existing knowledge models is illustrated in a game-theoretic application concerning the epistemic justification of iterative solution concepts.     

An epistemic model of an agent who does not reflect on reasoning processes

This paper introduces an epistemic model of a boundedly rational agent under the two assumptions that (i) the agent’s reasoning process is in accordance with the model but (ii) the agent does not reflect on these reasoning processes. For such a concept of bounded rationality a semantic interpretation by the possible world semantics of the Kripke (1963) type is no longer available because the definition of knowledge in these possible world semantics implies that the agent knows all valid statements of the model. The key to my alternative semantic approach is the extension of the method of truth tables, first introduced for the propositional logic by Wittgenstein (1922), to an epistemic logic so that I can determine the truth value of epistemic statements for all relevant truth conditions. In my syntactic approach I define an epistemic logic–consisting of the classical calculus of propositional logic plus two knowledge axioms–that does not include the inference rule of necessitation, which claims that an agent knows all theorems of the logic. As my main formal result I derive a determination theorem linking my semantic with my syntactic approach. The difference between my approach and existing knowledge models is illustrated in a game-theoretic application concerning the epistemic justification of iterative solution concepts.     

∧~*系统的公理化扩张

通过对模糊逻辑命题演算形式系统L*的代数语义——R0代数的研究,给出了R0代数簇的完整分类,并利用L*系统与幂零极小逻辑(NML)的等价性,由系统L*是可代数化逻辑出发,得到与R0代数真子簇对应的L*系统的全部公理化扩张,文中所用的方法用样适用于其他满足逆序对合关系的逻辑的扩张,具有较好的扩展性。     

ON THE RELIABILITY OF MEDIUM LOGIC(ML)

Medium logic (ML) is set up for the common theoritical foundation of the classical mathematics and fuzzy mathematics. It has been formalized as a new theory of logic. See note (1) and note (2). As mathematical logic the ML's construct reches the study of the informal deductive inference by means of studying the formal inference in it, and it demands the formal inference of ML reliable reflected the deductive inference. For this reason, this paper deals with its reliability. The result shows that the formal inference of M L consists with deductive inference, and that ML reliably reflects the deductive inference.     

A generalized time quantifier approach to approximate reasoning

In this paper, a rather expressive fuzzy temporal logic for linear time is introduced. First, this logic is a multivalued generalization (Lukasiewicz style) of a two-valued linear-time temporal logic based on, e.g., the “until” operator. Second, it is obtained by introducing a generalized time quantifier (a generalization of the partition operator investigated by Shen) applied to fuzzy time sets.In this fuzzy temporal logic, generalized compositional rules of inference, suitable for approximate reasoning in a temporal setting, are presented as valid formulas.Some medical examples illustrate our approach.     

Feasible algorithms for approximate reasoning using fuzzy logic

Deductive reasoning with classical logic is hampered when imprecision is present in the variables, although human reasoning can cope quite adequately with vague concepts. A new approach to reasoning which allows imprecise conclusions to be drawn consistently from imprecise premises was introduced by Baldwin [2]. This method is economical in calculation as it avoids the high dimensionality that fuzzy set representations often involve.This paper briefly reviews the method from an operational viewpoint, isolating the individual processes that are used in the method. A feasible algorithm for computing each process is then presented.It is assumed that the reader is familiar with the concept of, and operations on, fuzzy sets introduced by Zadeh [14].     

A method of inference in approximate reasoning based on interval-valued fuzzy sets

This paper introduces and discusses a method of approximate inference which operates on the extension of the concept of a fuzzy set by the concept of an interval-valued fuzzy set. This method allows a formal, fuzzy representation to be built for verbal decision algorithms. Furthermore, it can have an effective computer representation. An example showing how this method operates is provided.     

Probabilistic stit logic and its decomposition

We define an extension of stit logic that encompasses subjective probabilities representing beliefs about simultaneous choice exertion of other agents. This semantics enables us to express that an agent sees to it that a condition obtains under a minimal chance of success. We first define the fragment of XSTIT where choice exertion is not collective. Then we add lower bounds for the probability of effects to the stit syntax, and define the semantics of the newly formed stit operator in terms of subjective probabilities concerning choice exertion of other agents. We show how the resulting probabilistic stit logic faithfully generalizes the non-probabilistic XSTIT fragment. In a second step we analyze the defined probabilistic stit logic by decomposing it into an XSTIT fragment and a purely epistemic fragment. The resulting epistemic logic for grades of believes is a weak modal logic with a neighborhood semantics combining probabilistic and modal logic theory.     

Intuitionistic Fuzzy Logic Control for Heater Fans

The concept of intuitionistic fuzzy systems, including intuitionistic fuzzy sets and intuitionistic fuzzy logic, was introduced by Atanassov as a generalization of fuzzy systems. Intuitionistic fuzzy systems provide a mechanism for communication between computing systems and humans. In this paper, we describe the development of an intuitionistic fuzzy logic controller for heater fans, developed on the basis of intuitionistic fuzzy systems. Intuitionistic fuzzy inference systems and defuzzification techniques are used to obtain crisp output (i.e., speed of the heater fan) from an intuitionistic fuzzy input (i.e., ambient temperature). The speed of the heater fan is calculated using intuitionistic fuzzy rules applied in an inference engine using defuzzification methods.     

A probabilistic logic based on the acceptability of gambles

This article presents a probabilistic logic whose sentences can be interpreted as asserting the acceptability of gambles described in terms of an underlying logic. This probabilistic logic has a concrete syntax and a complete inference procedure, and it handles conditional as well as unconditional probabilities. It synthesizes Nilsson’s probabilistic logic and Frisch and Haddawy’s anytime inference procedure with Wilson and Moral’s logic of gambles.Two distinct semantics can be used for our probabilistic logic: (1) the measure–theoretic semantics used by the prior logics already mentioned and also by the more expressive logic of Fagin, Halpern, and Meggido and (2) a behavioral semantics. Under the measure–theoretic semantics, sentences of our probabilistic logic are interpreted as assertions about a probability distribution over interpretations of the underlying logic. Under the behavioral semantics, these sentences are interpreted only as asserting the acceptability of gambles, and this suggests different directions for generalization.     

A simple logic for reasoning about incomplete knowledge

The semantics of modal logics for reasoning about belief or knowledge is often described in terms of accessibility relations, which is too expressive to account for mere epistemic states of an agent. This paper proposes a simple logic whose atoms express epistemic attitudes about formulae expressed in another basic propositional language, and that allows for conjunctions, disjunctions and negations of belief or knowledge statements. It allows an agent to reason about what is known about the beliefs held by another agent. This simple epistemic logic borrows its syntax and axioms from the modal logic KD. It uses only a fragment of the S5 language, which makes it a two-tiered propositional logic rather than as an extension thereof. Its semantics is given in terms of epistemic states understood as subsets of mutually exclusive propositional interpretations. Our approach offers a logical grounding to uncertainty theories like possibility theory and belief functions. In fact, we define the most basic logic for possibility theory as shown by a completeness proof that does not rely on accessibility relations.     

Dynamic linear time temporal logic

A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic. It is shown that DLTL, the resulting logic, is expressively equivalent to the monadic second-order theory of ω-sequences. In fact, a sublogic of DLTL which corresponds to propositional dynamic logic with a linear time semantics is already expressively complete. We show that DLTL has an exponential time decision procedure and admits a finitary axiomatization. We also point to a natural extension of the approach presented here to a distributed setting.     

The systems approach and fuzzy set theory bridging the gap between mathematical and language-oriented economists

Ideas are presented to show how fuzzy mathematics can be applied in macro-economics in combination with the systems approach in order to bridge the gap between mathematical and language-oriented economists.Two reasons are given.From a mathematical point of view, fuzzy sets, fuzzy relations and fuzzy logic are not fuzzy at all. They are all well defined, but tend to be more complicated than traditional, mathematical concepts used in economics.From a language-oriented economist's point of view, fuzzy sets, etc. are used to express mathematically the type of concepts which are typical in language and most valuable in dealing with complex systems like an economy.The paper deals with economics in general terms, but examples are provided to illustrate the ideas.     

House of quality: A fuzzy logic-based requirements analysis

House Of Quality (HOQ) is one of the matrices of an iterative process called Quality Function Deployment (QFD). The foundation of the HOQ is the belief that products should be designed to reflect customers' desires and taste. HOQ is performed by a multidisciplinary team representing marketing, design engineering, manufacturing engineering, and any other functions considered critical by the company. In general, it provides a framework in which all participants can communicate their thoughts about a product. More specifically, HOQ is often used to identify the relationships between requirements based on different viewpoints. There are two issues in analyzing these requirements using HOQ. First, requirements are often described informally using vague terms. However, lack of formal way in interpreting the semantics of these requirements makes it difficult to determine if a realization of the system meets its customer's needs. Second, identifying relationships between requirements is often time consuming. Sometimes, it is difficult to arrive at a group consensus on a particular relationship between requirements. To address these issues, we have developed a fuzzy logic-based extension to HOQ for capturing imprecise requirements to both facilitate communication of team members and have a formal representation of requirements. Based on this representation, we developed a heuristic inference scheme to reason about the implicit relationships between requirements. We illustrate our approach using a textile mill supply business application.     

Some kinds of falling fuzzy filters of lattice implication algebras

In this paper, the concepts of falling fuzzy(implicative, associative) filters of lattice implication algebras based on the theory of falling shadows and fuzzy sets are presented at first. And then the relations between fuzzy(implicative, associative) filters and falling fuzzy(implicative, associative) filters are provided. In particular, we put forward an open question on a kind of falling fuzzy filters of lattice implication algebras. Finally, we apply falling fuzzy inference relations to lattice implication algebras and obtain some related results.     

L~*系统的一种改进系统L_0~*

研究了王国俊教授建立的模糊命题演算的形式演绎系统 L*以及在语义上相关的修正的 Kleene逻辑系统 W,W,Wk,给出了 L*系统的一种改进系统 L*0 ,并证明了二者之间的等价性 ,为形式演绎系统 L* 的研究和应用提供了一个有益的途径     

Actualism and Modal Semantics

According to actualism, modal reality is constructed out of valuations (combinations of truth values for all propositions). According to possibilism, modal reality consists in a set of possible worlds, conceived as independent objects that assign truth values to propositions. According to possibilism, accounts of modal reality can intelligibly disagree with each other even if they agree on which valuations are contained in modal reality. According to actualism, these disagreements (possibilist disagreements) are completely unintelligible. An essentially actualist semantics for modal propositional logic specifies which sets of valuations are compatible with the meanings of the truth-functional connectives and modal operators without drawing on formal resources that would enable us to represent possibilist disagreements. The paper discusses the availability of an essentially actualist semantics for modal propositional logic. I argue that the standard Kripkean semantics is not essentially actualist and that other extant approaches also fail to provide a satisfactory essentially actualist semantics. I end by describing an essentialist actualist semantics for modal propositional logic.     

On the equivalence between logic programming semantics and argumentation semantics

In the current paper, we re-examine the connection between formal argumentation and logic programming from the perspective of semantics. We observe that one particular translation from logic programs to instantiated argumentation (the one described by Wu, Caminada and Gabbay) is able to serve as a basis for describing various equivalences between logic programming semantics and argumentation semantics. In particular, we are able to show equivalence between regular semantics for logic programming and preferred semantics for formal argumentation. We also show that there exist logic programming semantics (L-stable semantics) that cannot be captured by any abstract argumentation semantics.     

Uncertain inference control for balancing an inverted pendulum

Fuzzy inference control uses fuzzy sets to describe the antecedents and consequents of If-Then rules. However, most surveys show the antecedents and consequents are uncertain sets rather than fuzzy sets. This fact provides a motivation to invent an uncertain inference control method. This paper gives an introduction to the design procedures of uncertain inference controller. As an example, an uncertain inference controller for balancing an inverted pendulum system is successfully designed. The computer simulation shows the developed uncertain inference controller is of good robustness.