Lattice-based Graded Logic: A Multimodal Approach
نویسندگان
چکیده
Experts do not always feel very comfortable when they ha vt! to give precise nunterica I estimations of cena inty degrees. In this paper we present a qualitative approach which allows for atraching parti ally ordered symbolic grades to logical formulas. Uncertain inform ati on is expressed by means of parameterized mod a I operators. We propo se a sema ntics for this multimodal logic and give a sound and complete axiomatization. We study the links with rela ted approaches and suggest how this frame work might be used to manage hoth uncerta in and incomplere knowledge.
منابع مشابه
Characterizing Fuzzy Modal Semantics by Fuzzy Multimodal Systems with Crisp Accessibility Relations
In [1] the authors considered finitely-valued modal logics with Kripke style semantics where both propositions and the accessibility relation are valued over a finite residuated lattice. Unfortunately, the necessity operator does not satisfy in general the normality axiom (K). In this paper we focus on the case of finite chains, and we consider a different approach based on introducing a multim...
متن کاملT-norm-based Fuzzy Logics and Logics for Human Reasoning
In [1] the authors considered finitely-valued modal logics with Kripke style semantics where both propositions and the accessibility relation are valued over a finite residuated lattice. Unfortunately, the necessity operator does not satisfy in general the normality axiom (K). In this paper we focus on the case of finite chains, and we consider a different approach based on introducing a multim...
متن کاملTREE AUTOMATA BASED ON COMPLETE RESIDUATED LATTICE-VALUED LOGIC: REDUCTION ALGORITHM AND DECISION PROBLEMS
In this paper, at first we define the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write $mathcal{L}$-valued) tree automaton with a threshold $c.$ Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as finiteness-value and emptiness-value of recognizable t...
متن کاملModifier Logics Based on Graded Modalities
Modifier logics are considered as generalizations of "classiea1" modal logics. Thus modifier logics are soeanled multimodal logios. Multimodality means here that the basic logics are modal logics with graded modalities. The interpretation of modal operators is more generan, too. Leibniz's mottvating semantical ideas (see [8]. p. 20-21) givejustification to these generalizations. Semantics of ca...
متن کاملFuzzy inequational logic
We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes their semantic entailment and provability in graded setting which allows to draw partially true conclusions from partially true assumptions. We follow the Pa...
متن کامل