Molecular Biology Meets Logic : Context-Sensitiveness in Focus

Some real life processes, including molecular ones, are context-sensitive, in the sense that their outcome depends on side conditions that are most of the times difficult, or impossible, to express fully in advance. In this paper, we survey and discuss a logical account of context-sensitiveness in molecular processes, based on a kind of non-classical logic. This account also allows us to revisit the relationship between logic and philosophy of science (and philosophy of biology, in particular)

Molecular biology meets Logic : context-sensitiveness in focus

Some real life processes, including molecular ones, are context-sensitive, in the sense that their outcome depends on side conditions that are most of the times difficult, or impossible, to express fully in advance. In this paper, we survey and discuss a logical account of context-sensitiveness in molecular processes, based on a kind of non-classical logic. This account also allows us to revisit the relationship between logic and philosophy of science (and philosophy of biology, in particular)

Sequences of refinements of rough sets: logical and algebraic aspects

In this thesis, a generalization of the classical Rough set theory is developed considering the so-called sequences of orthopairs that we define as special sequences of rough sets. Mainly, our aim is to introduce some operations between sequences of orthopairs, and to discover how to generate them starting from the operations concerning standard rough sets. Also, we prove several representation theorems representing the class of finite centered Kleene algebras with the interpolation property, and some classes of finite residuated lattices (more precisely, we consider Nelson algebras, Nelson lattices, IUML-algebras and Kleene lattice with implication) as sequences of orthopairs. Moreover, as an application, we show that a sequence of orthopairs can be used to represent an examiner's opinion on a number of candidates applying for a job, and we show that opinions of two or more examiners can be combined using operations between sequences of orthopairs in order to get a final decision on each candidate. Finally, we provide the original modal logic SOn with semantics based on sequences of orthopairs, and we employ it to describe the knowledge of an agent that increases over time, as new information is provided. Modal logic Son is characterized by the sequences (\u25a11,\u2026, \u25a1n) and (O1,\u2026, On) of n modal operators corresponding to a sequence (t1,\u2026, tn) of consecutive times. Furthermore, the operator \u25a1i of (\u25a11,\u2026, \u25a1n) represents the knowledge of an agent at time ti, and it coincides with the necessity modal operator of S5 logic. On the other hand, the main innovative aspect of modal logic SOn is the presence of the sequence (O1,\u2026, On), since Oi establishes whether an agent is interested in knowing a given fact at time ti

Sequences of refinements of rough sets: logical and algebraic aspects

In this thesis, a generalization of the classical Rough set theory is developed considering the so-called sequences of orthopairs that we define as special sequences of rough sets. Mainly, our aim is to introduce some operations between sequences of orthopairs, and to discover how to generate them starting from the operations concerning standard rough sets. Also, we prove several representation theorems representing the class of finite centered Kleene algebras with the interpolation property, and some classes of finite residuated lattices (more precisely, we consider Nelson algebras, Nelson lattices, IUML-algebras and Kleene lattice with implication) as sequences of orthopairs. Moreover, as an application, we show that a sequence of orthopairs can be used to represent an examiner's opinion on a number of candidates applying for a job, and we show that opinions of two or more examiners can be combined using operations between sequences of orthopairs in order to get a final decision on each candidate. Finally, we provide the original modal logic SOn with semantics based on sequences of orthopairs, and we employ it to describe the knowledge of an agent that increases over time, as new information is provided. Modal logic Son is characterized by the sequences (□1,…, □n) and (O1,…, On) of n modal operators corresponding to a sequence (t1,…, tn) of consecutive times. Furthermore, the operator □i of (□1,…, □n) represents the knowledge of an agent at time ti, and it coincides with the necessity modal operator of S5 logic. On the other hand, the main innovative aspect of modal logic SOn is the presence of the sequence (O1,…, On), since Oi establishes whether an agent is interested in knowing a given fact at time ti

Polarized substructural session types

Concurrent processes can be extremely difficult to reason about, both for programmers and formally. One approach to coping with this difficulty is to study new programming languages and type features such as Session Types. Session types take as their conceptual notion of concurrency as a collection of processes linked together via channels and provide type-level coordination between processes using these channels. Logically motivated programming languages exploit the idea that providing a proof of a theorem in a logic is similar to proving that a given term has a particular type in a programming language and vice versa. These connections can be interesting for a few different reasons. First, when language and logic are independently discovered and independently useful, the existence of a connection suggests that both are onto some fundamentally important idea. Additionally, a connection provides a basis both for sanity checking our ideas and also can be fruitful grounds for inspiration by seeing how variants of either the logic or the language are reflected through the connection. This thesis primarily describes an exploration of logically motivated session types, SILL. Polarization, classifying propositions as either positive or negative, provides a natural way to describe a logically based session typing language with asynchronous communication while retaining a semantics that is reasonably implementable. Additionally, polarization gives us a way to smoothly integrate synchronous channels into SILL without needing a semantic extension. When combined with Adjoint Logic, this gives us an ability to incorporate a variety of modalities with relatively little work. From a practical perspective, this gives SILL access to persistent processes and garbage collection. We additionally explore a trio of loosely related extensions to SILL, and their logical connections, inspired by the above results: bundled message passing to reduce the number of communications performed by processes; racy programs, enabled by a select/epoll-like mechanism; and asynchronous receiving, an almost generalization of the basic asynchronous semantics. We have three different implementations of SILL: a simple but relatively full featured interpreter written in OCaml; a fragment of SILL as an embedded domain specific language in Haskell; and a cleaner version of the same in Idris. Lastly, we show that Liquid Types and Session Types are compatible. This gives us one notion of a dependently session typed language

Circular Proofs as Session-Typed Processes: A Local Validity Condition

Proof theory provides a foundation for studying and reasoning about programming languages, most directly based on the well-known Curry-Howard isomorphism between intuitionistic logic and the typed lambda-calculus. More recently, a correspondence between intuitionistic linear logic and the session-typed pi-calculus has been discovered. In this paper, we establish an extension of the latter correspondence for a fragment of substructural logic with least and greatest fixed points. We describe the computational interpretation of the resulting infinitary proof system as session-typed processes, and provide an effectively decidable local criterion to recognize mutually recursive processes corresponding to valid circular proofs as introduced by Fortier and Santocanale. We show that our algorithm imposes a stricter requirement than Fortier and Santocanale's guard condition, but is local and compositional and therefore more suitable as the basis for a programming language.Comment: The revised version, 48 pages, submitted to Logical Methods in Computer Scienc