Exclusion Problems and the Cardinality of Logical Space

Wittgenstein’s atomist picture, as embodied in his Tractatus, is initially very appealing. However, it faces the famous colour-exclusion problem. In this paper, I shall explain when the atomist picture can be defended (in principle) in the face of that problem; and, in the light of this, why the atomist picture should be rejected. I outline the atomist picture in Section 1. In Section 2, I present a very simple necessary and sufficient condition for the tenability (in principle) of the atomist picture. The condition is: $\textit{logical space is a power of two}$. In Sections 3 and 4, I outline the colour-exclusion problem, and then show how the cardinality-condition supplies a response to exclusion problems. In Section 5, I explain how this amounts to a distillation of a proposal due to Moss (2012), which goes back to Carruthers (1990: 144–7). And in Section 6, I show how all this vindicates Wittgenstein’s ultimate rejection of the atomist picture. The brief reason is that we have no guarantee that there are any solutions to a given exclusion problem but, if there are any, then there are far too many.Funded by a Philip Leverhulme Prize, awarded by the Leverhulme Trust, PLP–2014–140.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s10992-016-9412-

An Ontological formalization of the planning task

In this paper we propose a generic task ontology, which formalizes the space of planning problems. Although planning is one of the oldest researched areas in Artificial Intelligence and attempts have been made in the past at developing task ontologies for planning, these formalizations suffer from serious limitations: they do not exhibit the required level of formalization and precision and they usually fail to include some of the key concepts required for specifying planning problems. In con-trast with earlier proposals, our task ontology formalizes the nature of the planning task independently of any planning paradigm, specific domains, or applications and provides a fine-grained, precise and comprehensive characterization of the space of planning problems. Finally, in addition to producing a formal specification we have also operationalized the ontology into a set of executable definitions, which provide a concrete reusable resource for knowledge acquisition and system development in planning applications

The logic of forbidden colours

The purpose of this paper is twofold: (1) to clarify Ludwig Wittgenstein’s thesis that colours possess logical structures, focusing on his ‘puzzle proposition’ that “there can be a bluish green but not a reddish green”, (2) to compare modeltheoretical and gametheoretical approaches to the colour exclusion problem. What is gained, then, is a new gametheoretical framework for the logic of ‘forbidden’ (e.g., reddish green and bluish yellow) colours. My larger aim is to discuss phenomenological principles of the demarcation of the bounds of logic as formal ontology of abstract objects

Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis

The safety of infinite state systems can be checked by a backward reachability procedure. For certain classes of systems, it is possible to prove the termination of the procedure and hence conclude the decidability of the safety problem. Although backward reachability is property-directed, it can unnecessarily explore (large) portions of the state space of a system which are not required to verify the safety property under consideration. To avoid this, invariants can be used to dramatically prune the search space. Indeed, the problem is to guess such appropriate invariants. In this paper, we present a fully declarative and symbolic approach to the mechanization of backward reachability of infinite state systems manipulating arrays by Satisfiability Modulo Theories solving. Theories are used to specify the topology and the data manipulated by the system. We identify sufficient conditions on the theories to ensure the termination of backward reachability and we show the completeness of a method for invariant synthesis (obtained as the dual of backward reachability), again, under suitable hypotheses on the theories. We also present a pragmatic approach to interleave invariant synthesis and backward reachability so that a fix-point for the set of backward reachable states is more easily obtained. Finally, we discuss heuristics that allow us to derive an implementation of the techniques in the model checker MCMT, showing remarkable speed-ups on a significant set of safety problems extracted from a variety of sources.Comment: Accepted for publication in Logical Methods in Computer Scienc

Labels for non-individuals

Quasi-set theory is a first order theory without identity, which allows us to cope with non-individuals in a sense. A weaker equivalence relation called ``indistinguishability'' is an extension of identity in the sense that if $x$ is identical to $y$ then $x$ and $y$ are indistinguishable, although the reciprocal is not always valid. The interesting point is that quasi-set theory provides us a useful mathematical background for dealing with collections of indistinguishable elementary quantum particles. In the present paper, however, we show that even in quasi-set theory it is possible to label objects that are considered as non-individuals. We intend to prove that individuality has nothing to do with any labelling process at all, as suggested by some authors. We discuss the physical interpretation of our results.Comment: 11 pages, no figure

Analysis of methods

Information is one of an organization's most important assets. For this reason the development and maintenance of an integrated information system environment is one of the most important functions within a large organization. The Integrated Information Systems Evolution Environment (IISEE) project has as one of its primary goals a computerized solution to the difficulties involved in the development of integrated information systems. To develop such an environment a thorough understanding of the enterprise's information needs and requirements is of paramount importance. This document is the current release of the research performed by the Integrated Development Support Environment (IDSE) Research Team in support of the IISEE project. Research indicates that an integral part of any information system environment would be multiple modeling methods to support the management of the organization's information. Automated tool support for these methods is necessary to facilitate their use in an integrated environment. An integrated environment makes it necessary to maintain an integrated database which contains the different kinds of models developed under the various methodologies. In addition, to speed the process of development of models, a procedure or technique is needed to allow automatic translation from one methodology's representation to another while maintaining the integrity of both. The purpose for the analysis of the modeling methods included in this document is to examine these methods with the goal being to include them in an integrated development support environment. To accomplish this and to develop a method for allowing intra-methodology and inter-methodology model element reuse, a thorough understanding of multiple modeling methodologies is necessary. Currently the IDSE Research Team is investigating the family of Integrated Computer Aided Manufacturing (ICAM) DEFinition (IDEF) languages IDEF(0), IDEF(1), and IDEF(1x), as well as ENALIM, Entity Relationship, Data Flow Diagrams, and Structure Charts, for inclusion in an integrated development support environment