Proof Systems for Reasoning about Computation Errors

In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued Kleene logic can be used for reasoning about parallel computation. If we want to be able to deal with both strategies without distinguishing between them, we combine Kleene and McCarthy logics into a logic based on a non-deterministic, 3-valued matrix, incorporating both options as a non-deterministic choice. If the two strategies are to be distinguished, Kleene and McCarthy logics are combined into a logic based on a 4-valued deterministic matrix featuring two kinds of computation errors which correspond to the two computation strategies described above. For the resulting logics, we provide sound and complete calculi of ordinary, two-valued sequents. Presented by Yaroslav Shramko and Heinrich Wansing     

On Consistent Subsets of Large Sets of Satisfiable Sentences

We extend some results of Adam Kolany to show that large sets of satisfiable sentences generally contain equally large subsets of mutually consistent sentences. In particular, this is always true for sets of uncountable cofinality, and remains true for sets of denumerable cofinality if we put appropriate bounding conditions on the sentences. The results apply to both the propositional and the predicate calculus. To obtain these results, we use delta sets for regular cardinals, and, for singular cardinals, a generalization of delta sets. All of our results are theorems in ZFC.     

A logical calculus for controlled monotonicity

In this paper we introduce a new deductive framework for analyzing processes displaying a kind of controlled monotonicity. In particular, we prove the cut-elimination theorem for a calculus involving series-parallel structures over partial orders which is built up from multi-level sequents, an interesting variant of Gentzen-style sequents. More broadly, our purpose is to provide a general, syntactical tool for grasping the combinatorics of non-monotonic processes.     

Cut-Free Tableau Calculi for some Intuitionistic Modal Logics

In this paper we provide cut-free tableau calculi for the intuitionistic modal logics IK, ID, IT, i.e. the intuitionistic analogues of the classical modal systems K, D and T. Further, we analyse the necessity of duplicating formulas to which rules are applied. In order to develop these calculi we extend to the modal case some ideas presented by Miglioli, Moscato and Ornaghi for intuitionistic logic. Specifically, we enlarge the language with the new signs Fc and CR near to the usual signs T and F. In this work we establish the soundness and completeness theorems for these calculi with respect to the Kripke semantics proposed by Fischer Servi.     

A Proof-theoretical Analysis of Semiconstructive Intermediate Theories

In the 80's Pierangelo Miglioli, starting from motivations in the framework of Abstract Data Types and Program Synthesis, introduced semiconstructive theories, a family of large subsystems of classical theories that guarantee the computability of functions and predicates represented by suitable formulas. In general, the above computability results are guaranteed by algorithms based on a recursive enumeration of the theorems of the whole system. In this paper we present a family of semiconstructive systems, we call uniformly semiconstructive, that provide computational procedures only involving formulas with bounded complexity. We present several examples of uniformly semiconstructive systems containing Harrop theories, induction principles and some well-known predicate intermediate principles. Among these, we give an account of semiconstructive and uniformly semiconstructive systems which lie between Intuitionistic and Classical Arithmetic and we discuss their constructive incompatibility.     

On Finite Models of the Lambek Calculus

We study a class of finite models for the Lambek Calculus with additive conjunction and with and without empty antecedents. The class of models enables us to prove the finite model property for each of the above systems, and for some axiomatic extensions of them. This work strengthens the results of [3] where only product-free fragments of these systems are considered. A characteristic feature of this approach is that we do not rely on cut elimination in opposition to e.g. [5], [9].     

Axiomatizing hybrid products: How can we reason many-dimensionally in hybrid logic?

The aim of this paper is to propose a two-dimensional hybrid logic in order to formalize inferences containing both spatial and temporal propositions. The semantic idea behind the proposal is to name both horizontal and vertical lines in a 2D-plane by two kinds of nominals. This is a generalization of the idea of naming a point in one-dimensional hybrid logic. I give an axiomatization of the proposed two-dimensional hybrid logic and show that it enjoys a general completeness result (called pure completeness) with respect to product Kripke frames. Moreover, in order to capture $T\times W$-frames studied by R.H. Thomason (1984), I introduce the notion of a dependent product frame, which enables us to represent the dependence of space over time. I also give a complete axiomatization of this dependent two-dimensional hybrid logic, and, as a corollary, reveal that a hybridization of $T\times W$-logic enjoys strong completeness.     

机器学习在解决过拟合现象中的作用

过拟合现象是心理学走向预测科学的重要阻碍。文章综述了机器学习在解决过拟合现象中的价值和实现途径：（1）介绍了过拟合的两种表现形式和现状;（2）分析过拟合的根因,即“高解释力≠高预测力”;（3）厘清机器学习的建模逻辑与核心技术在解决过拟合中的作用;（4）利用样例数据和代码说明机器学习统计思想在模型拟合中的具体应用过程。文章指出心理学应从解决实际问题的角度出发,借鉴机器学习的分析思想,避免过拟合,进而提供更准确更稳定的结论和预测模型。