We provide a full characterization of computational error states for information systems. The class of errors considered is general enough to include human rational processes, logical reasoning, scientific progress and data processing in some functional programming languages. The aim is to reach a full taxonomy of error states by analysing the recovery and processing of data. We conclude by presenting machine-readable checking and resolve algorithms.

In this paper we examine two approaches to the formal treatment of the notion of problem in the paradigm of algorithmic semantics. Namely, we will explore an approach based on Martin-Löf’s Constructive Type Theory, which can be seen as a direct continuation of Kolmogorov’s original calculus of problems, and an approach utilizing Tichý’s Transparent Intensional Logic, which can be viewed as a non-constructive attempt of interpreting Kolmogorov’s logic of problems. In the last section we propose Kolmogorov and CTT-inspired modifications to (...) TIL-based approach. The focus will be on non-empirical problems only. (shrink)

I present an analysis according to which the current state of the definition of substitution leads to a contradiction in the system of Transparent Intensional Logic. I entail the contradiction using only the basic definitions of TIL and standard results. I then analyse the roots of the contradiction and motivate the path I take in resolving the contradiction. I provide a new amended definition of collision-less substitution which blocks the contradiction in a non-ad hoc way. I elaborate on the consequences (...) of the amended definition, namely the invalidity of the Church-Rosser theorem. I present a counterexample to the validity of the theorem in TIL with an amended definition of substitution. (shrink)

This paper presents several important results for Transparent Intensional Logic. The conversions that are standardly taken to be valid – namely restricted β-conversion by name and β-reduction...

In a 2010 paper Daley argues, contra Fodor, that several syntactically simple predicates express structured concepts. Daley develops his theory of structured concepts within Tichý’s Transparent Intensional Logic . I rectify various misconceptions of Daley’s concerning TIL. I then develop within TIL an improved theory of how structured concepts are structured and how syntactically simple predicates are related to structured concepts.

A property modifier is a function that takes a property to a property. For instance, the modifier short takes the property being a Dutchman to the property being a short Dutchman. Assume that being a round peg is a property obtained by means of modification, round being the modifier and being a peg the input property. Then how are we to infer that a round peg is a peg? By means of a rule of right subsectivity. How are we to (...) infer that a round peg is round? By means of a rule of left subsectivity. This paper puts forward two rules of left subsectivity. The rules fill a gap in the prevalent theory of property modification. The paper also explains why the rules are philosophically relevant. (shrink)

The standard rule of single privative modification replaces privative modifiers by Boolean negation. This rule is valid, for sure, but also simplistic. If an individual a instantiates the privatively modified property (MF) then it is true that a instantiates the property of not being an F, but the rule fails to express the fact that the properties (MF) and F have something in common. We replace Boolean negation by property negation, enabling us to operate on contrary rather than contradictory properties. (...) To this end, we apply our theory of intensional essentialism, which operates on properties (intensions) rather than their extensions. We argue that each property F is necessarily associated with an essence, which is the set of the so-called requisites of F that jointly define F. Privation deprives F of some but not all of its requisites, replacing them by their contradictories. We show that properties formed from iterated privatives, such as being an imaginary fake banknote, give rise to a trifurcation of cases between returning to the original root property or to a property contrary to it or being semantically undecidable for want of further information. In order to determine which of the three forks the bearers of particular instances of multiply modified properties land upon we must examine the requisites, both of unmodified and modified properties. Requisites underpin our presuppositional theory of positive predication. Whereas privation is about being deprived of certain properties, the assignment of requisites to properties makes positive predication possible, which is the predication of properties the bearers must have because they have a certain property formed by means of privation. (shrink)

In this paper we investigate how inference to the best explanation works in engineering science, focussing on the context of malfunction explanation. While IBE has gotten a lot of attention in the philosophy of science literature, few, if any, philosophical work has focussed on IBE in engineering science practice. We first show that IBE in engineering science has a similar structure as IBE in other scientific domains in the sense that in both settings IBE hinges on the weighing of explanatory (...) virtues. We then proceed to show that, due to the intimate connection between explanation and redesign in engineering science, there is a further engineering domain-specific virtue in terms of which engineering malfunction explanations are evaluated, viz. the virtue of redesign utility. This virtue entails that the explanatory information offered by a malfunction explanation should be instrumental in predicting counterfactual dependencies in redesigned systems. We illustrate and elaborate these points in terms of a number of engineering examples, focussing in particular on the 2009 crash of Air France Flight 447. Our extension of analyses of IBE and explanation to engineering science practice offers new insights by identifying a new explanatory virtue in malfunction explanation: redesign utility. (shrink)