纤维逻辑

形式逻辑已经从简单命题逻辑发展到比较复杂的模态逻辑系列。但是在主体环境下,已有逻辑的复杂性仍然不能有效刻画主体复杂的心智。有一些人工智能研究者根据主体心智的多重性,在模态逻辑中引入多种模态算子,并借此对主体加以刻画。但是原来的可能世界语义却难以容纳如此复杂的语法,出现了很多不合理的地方。本文首先介绍了新近出现的纤维逻辑（fibring logics）,然后归纳了目前将此理论应用在主体BDI建模的研究现状,最后分析纤维逻辑的不足之处,讨论了其他可能的应用,并对今后的工作做了展望。     

Fibring Non-Truth-Functional Logics: Completeness Preservation

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. This completeness transfer result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established.     

Eulogy: Dov Chevion, 1917-1983

Dov Chevion was a giant among his fellow men and women. He was respected for his strength of leadership, for his commitment toward worthy goals, and as the spokesman in the computer field for Israel for over two decades. He was particularly concerned with education, an area in which he made major contributions.     

Local Logics, Non-Monotonicity and Defeasible Argumentation

In this paper we present an embedding of abstract argumentation systems into the framework of Barwise and Seligmans logic of information flow. We show that, taking P.M. Dungs characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dungs extensions of argument systems leads to a corresponding ordering of background conditions. The relations among extensions becomes a relation among partial orderings of background conditions. This introduces a conceptual innovation in Barwise and Seligmans representation of commonsense reasoning.     

Local Logics, Non-Monotonicity and Defeasible Argumentation

In this paper we present an embedding of abstract argumentation systems into the framework of Barwise and Seligman’s logic of information flow. We show that, taking P.M. Dung’s characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dung’s extensions of argument systems leads to a corresponding ordering of background conditions. The relations among extensions becomes a relation among partial orderings of background conditions. This introduces a conceptual innovation in Barwise and Seligman’s representation of commonsense reasoning.     

Inessential Features, Ineliminable Features, and Modal Logics for Model Theoretic Syntax

While monadic second-order logic (MSO) has played a prominent role in model theoretic syntax, modal logics have been used in this context since its inception. When comparing propositional dynamic logic (PDL) to MSO over trees, Kracht (1997) noted that there are tree languages that can be defined in MSO that can only be defined in PDL by adding new features whose distribution is predictable. He named such features “inessential features”. We show that Kracht’s observation can be extended to other modal logics of trees in two ways. First, we demonstrate that for each stronger logic, there exists a tree language that can only be defined in a weaker logic with inessential features. Second, we show that any tree language that can be defined in a stronger logic, but not in some weaker logic, can be defined with inessential features. Additionally, we consider Kracht’s definition of inessential features more closely. It turns out that there are features whose distribution can be predicted, but who fail to be inessential in Kracht’s sense. We will look at ways to modify his definition.     

Possibility Theory, Probability Theory and Multiple-Valued Logics: A Clarification

There has been a long-lasting misunderstanding in the literature of artificial intelligence and uncertainty modeling, regarding the role of fuzzy set theory and many-valued logics. The recurring question is that of the mathematical and pragmatic meaningfulness of a compositional calculus and the validity of the excluded middle law. This confusion pervades the early developments of probabilistic logic, despite early warnings of some philosophers of probability. This paper tries to clarify this situation. It emphasizes three main points. First, it suggests that the root of the controversies lies in the unfortunate confusion between degrees of belief and what logicians call degrees of truth. The latter are usually compositional, while the former cannot be so. This claim is first illustrated by laying bare the non-compositional belief representation embedded in the standard propositional calculus. It turns out to be an all-or-nothing version of possibility theory. This framework is then extended to discuss the case of fuzzy logic versus graded possibility theory. Next, it is demonstrated that any belief representation where compositionality is taken for granted is bound to at worst collapse to a Boolean truth assignment and at best to a poorly expressive tool. Lastly, some claims pertaining to an alleged compositionality of possibility theory are refuted, thus clarifying a pervasive confusion between possibility theory axioms and fuzzy set basic connectives.     

Hyper-Contradictions, Generalized Truth Values and Logics of Truth and Falsehood

In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of “revenge Liar” arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets of higher-order values. This method is based on the concept of a multilattice. If the method is applied to the set of truth values of Belnap's “useful four-valued logic”, one obtains a trilattice, and, more generally, structures here called Belnap-trilattices. As in Priest's case, it is shown that the generalized truth values motivated by hyper-contradictions have no effect on the logic. Whereas Priest's construction in terms of designated truth values always results in his Logic of Paradox, the present construction in terms of truth and falsity orderings always results in First Degree Entailment. However, it is observed that applying the multilattice-approach to Priest's initial set of truth values leads to an interesting algebraic structure of a “bi-and-a-half” lattice which determines seven-valued logics different from Priest's Logic of Paradox.