Summary Street: Interactive Computer Support for Writing

Summary Street is educational software based on latent semantic analysis (LSA), a computer method for representing the content of texts. The classroom trial described here demonstrates the power of LSA to support an educational goal by providing automatic feedback on the content of students' summaries. Summary Street provides this feedback in an easy-to-grasp, graphic display that helps students to improve their writing across multiple cycles of writing and revision on their own before receiving a teacher's final evaluation. The software thus has the potential to provide students with extensive writing practice without increasing the teacher's workload. In classroom trials 6th-grade students not only wrote better summaries when receiving content-based feedback from Summary Street, but also spent more than twice as long engaged in the writing task. Specifically, their summaries were characterized by a more balanced coverage of the content than summaries composed without this feedback. Greater improvement in content scores was observed with texts that were difficult to summarize. Classroom implementation of Summary Street is discussed, including suggestions for instructional activities beyond summary writing.     

对认知逻辑一个新发展的若干省思

当代有关于外在世界的激进怀疑论者常利用知识封闭性原则去论证他们的立场。为了反驳这样的怀疑论,有些学者主张我们应该重新检视知识的标准,以便发现这些怀疑论论证中的问题,特别是知识封闭性原则是否成立的问题。在这些学者中,有两类极为受到重视:一类是主张知识的成立与否只涉及"相关的"可能性是否已被排除的相关选择理论学者,如D.Lewis、F.Dretske、和M.Heller,另一类则是主张知识的成立与否与某些虚拟条件是否为真有关的虚拟论者,如R.Nozick、E.Sosa、和K.De Rose。不幸的是,对于这两类理论的讨论往往流于直觉并因而缺乏逻辑的严谨性。为了弥补这个缺点,W.Holliday最近利用了两种新的形式化语意论去重新模塑上述两类理论,并严格证明了每种理论在知识封闭性问题上的逻辑结果。他的形式化工作和证明带来了极为严格而又丰硕的成果,本论文的主旨便在对Holliday这一个认知逻辑的新发展方向作出若干哲学与逻辑上的省思。     

Sequent-Calculi for Metainferential Logics

Studia Logica - In recent years, some theorists have argued that the clogics are not only defined by their inferences, but also by their metainferences. In this sense, logics that coincide in their...     

Logics for Epistemic Programs

We construct logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting. We formalize these changes by defining a notion of epistemic program. The languages are two-sorted sets that contain not only sentences but also actions or programs. This is as in dynamic logic, and indeed our languages are not significantly more complicated than dynamic logics. But the semantics is more complicated. In general, the semantics of an epistemic program is what we call aprogram model. This is a Kripke model of ‘actions’,representing the agents' uncertainty about the current action in a similar way that Kripke models of ‘states’ are commonly used in epistemic logic to represent the agents' uncertainty about the current state of the system. Program models induce changes affecting agents' information, which we represent as changes of the state model, called epistemic updates. Formally, an update consists of two operations: the first is called the update map, and it takes every state model to another state model, called the updated model; the second gives, for each input state model, a transition relation between the states of that model and the states of the updated model. Each variety of epistemic actions, such as public announcements or completely private announcements to groups, gives what we call an action signature, and then each family of action signatures gives a logical language. The construction of these languages is the main topic of this paper. We also mention the systems that capture the valid sentences of our logics. But we defer to a separate paper the completeness proof. The basic operation used in the semantics is called the update product. A version of this was introduced in Baltag et al. (1998), and the presentation here improves on the earlier one. The update product is used to obtain from any program model the corresponding epistemic update, thus allowing us to compute changes of information or belief. This point is of interest independently of our logical languages. We illustrate the update product and our logical languages with many examples throughout the paper.     

Algebras and Matrices for Annotated Logics

We study the matrices, reduced matrices and algebras associated to the systems SA_T of structural annotated logics. In previous papers, these systems were proven algebraizable in the finitary case and the class of matrices analyzed here was proven to be a matrix semantics for them.We prove that the equivalent algebraic semantics associated with the systems SA_T are proper quasivarieties, we describe the reduced matrices, the subdirectly irreducible algebras and we give a general decomposition theorem. As a consequence we obtain a decision procedure for these logics.     

Some Useful 16-Valued Logics: How a Computer Network Should Think

In Belnaps useful 4-valued logic, the set 2={T,F} of classical truth values is generalized to the set 4=(2)={,{T},{F},{T,F}}. In the present paper, we argue in favor of extending this process to the set 16=(4) (and beyond). It turns out that this generalization is well-motivated and leads from the bilattice FOUR₂ with an information and a truth-and-falsity ordering to another algebraic structure, namely the trilattice SIXTEEN₃ with an information ordering together with a truth ordering and a (distinct) falsity ordering. Interestingly, the logics generated separately by the algebraic operations under the truth order and under the falsity order in SIXTEEN₃ coincide with the logic of FOUR₂, namely first degree entailment. This observation may be taken as a further indication of the significance of first degree entailment. In the present setting, however, it becomes rather natural to consider also logical systems in the language obtained by combining the vocabulary of the logic of the truth order and the falsity order. We semantically define the logics of the two orderings in the extended language and in both cases axiomatize a certain fragment comprising three unary operations: a negation, an involution, and their combination. We also suggest two other definitions of logics in the full language, including a bi-consequence system. In other words, in addition to presenting first degree entailment as a useful 16-valued logic, we define further useful 16-valued logics for reasoning about truth and (non-)falsity. We expect these logics to be an interesting and useful instrument in information processing, especially when we deal with a net of hierarchically interconnected computers. We also briefly discuss Arielis and Avrons notion of a logical bilattice and state a number of open problems for future research.Dedicated to Nuel D. Belnap on the occasion of his 75th Birthday     

Natural Deduction for Non-Classical Logics

We present a framework for machine implementation of families of non-classical logics with Kripke-style semantics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of labelled formulae, and a theory of labels characterizing the properties of the Kripke models. By appropriate combinations we capture both partial and complete fragments of large families of non-classical logics such as modal, relevance, and intuitionistic logics. Our approach is modular and supports uniform proofs of soundness, completeness and proof normalization. We have implemented our work in the Isabelle Logical Framework.     

知道一个行动的逻辑(英文)

以活动为认知对象的逻辑还没有系统地建立。本文我们采用半无穷方法、自代入方法、固定点方法和拟赋值方法全面建立这样的逻辑,从而研究知道一个活动的各种逻辑特性。根据这些方法,我们分别提出四类刻画知道一个活动的逻辑系统和相应的语义,然后证明这些系统相对各自的语义是可靠和完全的。     

Logics for Qualitative Inductive Generalization

The paper contains a survey of (mainly unpublished) adaptive logics of inductive generalization. These defeasible logics are precise formulations of certain methods. Some attention is also paid to ways of handling background knowledge, introducing mere conjectures, and the research guiding capabilities of the logics.     

On AGM for Non-Classical Logics

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and what is still missing for each approach.     

Non-classical Metatheory for Non-classical Logics

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper is to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete.     

On the Existence of Continua of Logics Between Some Intermediate Predicate Logics

A method for constructing continua of logics squeezed between some intermediate predicate logics, developed by Suzuki [8], is modified and applied to intervals of the form [L, L+ ¬¬S], where Lis a predicate logic, Sis a closed predicate formula. This solves one of the problems from Suzuki's paper.     

Labelled Resolution for Classical and Non-classical Logics

Resolution is an effective deduction procedure for classical logic. There is no similar "resolution" system for non-classical logics (though there are various automated deduction systems). The paper presents resolution systems for intuistionistic predicate logic as well as for modal and temporal logics within the framework of labelled deductive systems. Whereas in classical predicate logic resolution is applied to literals, in our system resolution is applied to L(abelled) R(epresentation) S(tructures). Proofs are discovered by a refutation procedure defined on LRSs, that imposes a hierarchy on clause sets of such structures together with an inheritance discipline. This is a form of Theory Resolution. For intuitionistic logic these structures are called I(ntuitionistic) R(epresentation) S(tructures). Their hierarchical structure allows the restriction of unification of individual variables and/or constants without using Skolem functions. This structures must therefore be preserved when we consider other (non-modal) logics. Variations between different logics are captured by fine tuning of the inheritance properties of the hierarchy. For modal and temporal logics IRS's are extended to structures that represent worlds and/or times. This enables us to consider all kinds of combined logics.     

Complex Predicates and Logics for Properties and Relations

In this paper I present a formal language in which complex predicates stand for properties and relations, and assignments of denotations to complex predicates and assignments of extensions to the properties and relations they denote are both homomorphisms. This system affords a fresh perspective on several important philosophical topics, highlighting the algebraic features of properties and clarifying the sense in which properties can be represented by their extensions. It also suggests a natural modification of current logics of properties, one in which some complex predicates stand for properties while others do not.     

Displaying and Deciding Substructural Logics 1: Logics with Contraposition

Many logics in the relevant family can be given a proof theory in the style of Belnap's display logic (Belnap, 1982). However, as originally given, the proof theory is essentially more expressive than the logics they seek to model. In this paper, we consider a modified proof theory which more closely models relevant logics. In addition, we use this proof theory to show decidability for a large range of substructural logics.     

通过演绎方式得概称句推理的逻辑

基于[4]中的逻辑系统G,本文通过删减和增加公理及规则给出3个逻辑G0,GD和Gs,同时,我们通过对正常主项选择函数添加不同的条件给出与三个逻辑相应的不同的模型定义。其中,G0是GD和Gs的基础。这些逻辑的给出是为了刻画通过演绎方式得概称句的推理的局部推理。     

Proof-Theoretic Functional Completeness for the Hybrid Logics of Everywhere and Elsewhere

A hybrid logic is obtained by adding to an ordinary modal logic further expressive power in the form of a second sort of propositional symbols called nominals and by adding so-called satisfaction operators. In this paper we consider hybridized versions of S5 (“the logic of everywhere”) and the modal logic of inequality (“the logic of elsewhere”). We give natural deduction systems for the logics and we prove functional completeness results.     

涵义语义与关于概称句推理的词项逻辑

概称句推理具有以词项为单位的特征并且词项的涵义在其中起到了重要的作用。已有的处理用A一表达式表达涵义,不够简洁和自然。亚里斯多德三段论是一种词项逻辑,但它是外延的和单调的。这两方面的情况使得有必要考虑新的词项逻辑。涵义语义的基本观点是：语词首先表达的是涵义,通过涵义的作用,语词有了指称,表达概念。概称句三段论是更为常用的推理,有两个基本形式GAG和Gaa。在涵义语义的基础上建立的系统GAG和Gaa是关于这两种推理的公理系统。     

Duality for Lattice-Ordered Algebras and for Normal Algebraizable Logics

Part I of this paper is developed in the tradition of Stone-type dualities, where we present a new topological representation for general lattices (influenced by and abstracting over both Goldblatt's [17] and Urquhart's [46]), identifying them as the lattices of stable compact-opens of their dual Stone spaces (stability refering to a closure operator on subsets). The representation is functorial and is extended to a full duality.In part II, we consider lattice-ordered algebras (lattices with additional operators), extending the Jónsson and Tarski representation results [30] for Boolean algebras with Operators. Our work can be seen as developing, and indeed completing, Dunn's project of gaggle theory [13, 14]. We consider general lattices (rather than Boolean algebras), with a broad class of operators, which we dubb normal, and which includes the Jónsson-Tarski additive operators. Representation of l-algebras is extended to full duality.In part III we discuss applications in logic of the framework developed. Specifically, logics with restricted structural rules give rise to lattices with normal operators (in our sense), such as the Full Lambek algebras (F L-algebras) studied by Ono in [36]. Our Stone-type representation results can be then used to obtain canonical constructions of Kripke frames for such systems, and to prove a duality of algebraic and Kripke semantics for such logics.