A constructive modal semantics for contextual verification

This paper introduces a non-standard semantics for a modal version of constructive KT for contextual (assumptions-based) verification. The modal fragment expresses verifiability under extensions of contexts, enjoying adapted validity and (weak) monotonicity properties depending on satisfaction of the contextual data

Offline and online data: on upgrading functional information to knowledge

This paper addresses the problem of upgrading functional information to knowledge. Functional information is defined as syntactically well-formed, meaningful and collectively opaque data. Its use in the formal epistemology of information theories is crucial to solve the debate on the veridical nature of information, and it represents the companion notion to standard strongly semantic information, defined as well-formed, meaningful and true data. The formal framework, on which the definitions are based, uses a contextual version of the verificationist principle of truth in order to connect functional to semantic information, avoiding Gettierization and decoupling from true informational contents. The upgrade operation from functional information uses the machinery of epistemic modalities in order to add data localization and accessibility as its main properties. We show in this way the conceptual worthiness of this notion for issues in contemporary epistemology debates, such as the explanation of knowledge process acquisition from information retrieval systems, and open data repositories

A formal approach to vague expressions with indexicals

In this paper, we offer a formal approach to the scantily investigated problem of vague expressions with indexicals, in particular including the spatial indexical `here' and the temporal indexical `now'. We present two versions of an adaptive fuzzy logic extended with an indexical, formally expressed by a modifier as a function that applies to predicative formulas. In the first version, such an operator is applied to non-vague predicates. The modified formulas may have a fuzzy truth value and fit into a Sorites paradox. We use adaptive fuzzy logics as a reasoning tool to address such a paradox. The modifier enables us to offer an adequate explication of the dynamic reasoning process. In the second version, a different result is obtained for an indexical applied to a formula with a possibly vague predicate, where the resulting modified formula has a crisp value and does not add up to a Sorites paradox

Two type-theoretical approaches to privative modification

In this paper we apply two kinds of procedural semantics to the problem of privative modification. We do this for three reasons. The first reason is to launch a tough test case to gauge the degree of substantial agreement between a constructivist and a realist interpretation of a procedural semantics; the second is to extend Martin-Lof's Type Theory to privative modification, which is characteristic of natural language; the third reason is to sketch a positive characterization of privation

On the ontology of the computing process and the epistemology of the computed

Software-intensive science (SIS) challenges in many ways our current scientific methods. This affects significantly our notion of science and scientific interpretation of the world, driving at the same time the philosophical debate. We consider some issues prompted by SIS in the light of the philosophical categories of ontology and epistemology

Constructive contextual modal judgments for reasoning from open assumptions

Dependent type theories using a structural notion of context are largely explored in their applications to programming languages, but less investigated for knowledge representation purposes. In particular, types with modalities are already used for distributed and staged computation. This paper introduces a type system extended with judgmental modalities internalizing epistemically different modes of correctness to explore a calculus of provability from refutable assumptions

Epistemic Modalities

I present an analysis of the notion of epistemic modalities, based on an appropriate interpretation of two basic constructivist issues: verification and epistemic agency. Starting from an historical analysis of conditions for judgments, I analyze first the reading of necessity with respect to apodictic judgements, and then that of possibility with respect to hypothetical judgement. The analysis results in a formal treatment of rules for judgemental modal operators, whose aim is to preserve epistemic states corresponding to verified and unverified assumptions in contexts. In the conclusion, further tracks of research are indicated for designing a semantic framework and defining multi-agents systems

Software theory change for resilient near-complete specifications

Software evolution and its laws are essential for antifragile system design and development. In this paper we model early-stage perfective and corrective changes to software system architecture in terms of logical operations of expansion and safe contraction on a theory. As a result, we formulate an inference-based notion of property specification resilience for computational systems, intended as resistance to change. The individuated resilient core of a software system is used to characterize adaptability properties

Managing software uninstall with negative trust

A problematic aspect of software management systems in view of integrity preservation is the handling, approval, tracking and eventual execution of change requests. In the context of the relation between clients and repositories, trust can help identifying all packages required by the intended installation. Negative trust, in turn, can be used to approach the complementary problem induced by removing packages. In this paper we offer a logic for negative trust which allows to identify admissible and no-longer admissible software packages in the current installation profile in view of uninstall processes. We provide a simple working example and the system is formally verified using the Coq theorem prover

A typed natural deduction calculus to reason about secure trust

System integrity can be put at risk by unintentional transitivity of resource access. We present a natural deduction calculus for an access control model with an explicit trust function on resources. Its inference relation is designed to limit unintentionally transitive access from untrusted parties. We also offer results for ordered cut and normalization related to security and hint at a prototype implementation