Compositionality is not the problem

The paper analyses what is said and what is presupposed by the Principle of Compositionality for semantics, as it is commonly stated. The Principle of Compositionality is an axiom which some semantics satisfy and some don’t. It says essentially that if two expressions have the same meaning then they make the same contribution to the meanings of expressions containing them. This is a sensible axiom only if one combines it with (a) a converse, that if two expressions make the same contribution to the meanings of (say) sentences containing them, then they have the same meaning; and (b) some assumption that two expressions which can’t meaningfully be substituted for each other have different meanings. (The paper formalizes (a) as a full abstraction principle, and (b) as ‘Husserl’s principle’.) Moreover the Principle of Compositionality speaks only about when two expressions have the same meaning; it adds nothing whatever about what that meaning might be (the ‘representation problem’). Some recent discussions by writers in linguistics and logic are assessed. The paper finishes by reviewing the history of the notion of compositionality

Remark on Al-Fārābī's missing modal logic and its effect on Ibn Sīnā

We reconstruct as much as we can the part of al-Fārābī's treatment of modal logic that is missing from the surviving pages of his Long Commentary on the Prior Analytics. We use as a basis the quotations from this work in Ibn Sīnā, Ibn Rushd and Maimonides, together with relevant material from al-Fārābī's other writings. We present a case that al-Fārābī's treatment of the dictum de omni had a decisive effect on the development and presentation of Ibn Sīnā's modal logic. We give further evidence that the Harmonisation of the Opinions of Plato and Aristotle was not written by al-Fārābī

Naturality and Definability, I

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135298/1/jlms0001.pd

Preface

The 14th International Congress of Logic, Methodology and Philosophy of Science was held in July, 19th – 26th, 2011 in Nancy, the historic capital of Lorraine and birthplace of Henri Poincaré. We were very honored that the President of the French Republic, Monsieur Nicolas Sarkozy, generously agreed his patronage. The LMPS congresses represent the current state of the art and offer new perspectives in its fields. There were 900 registered participants from 56 different countries. They filled ..

Preface

The 14th International Congress of Logic, Methodology and Philosophy of Science was held in July, 19th – 26th, 2011 in Nancy, the historic capital of Lorraine and birthplace of Henri Poincaré. We were very honored that the President of the French Republic, Monsieur Nicolas Sarkozy, generously agreed his patronage. The LMPS congresses represent the current state of the art and offer new perspectives in its fields. There were 900 registered participants from 56 different countries. They filled ..

Preface

The 14th International Congress of Logic, Methodology and Philosophy of Science was held in July, 19th – 26th, 2011 in Nancy, the historic capital of Lorraine and birthplace of Henri Poincaré. We were very honored that the President of the French Republic, Monsieur Nicolas Sarkozy, generously agreed his patronage. The LMPS congresses represent the current state of the art and offer new perspectives in its fields. There were 900 registered participants from 56 different countries. They filled..

Generating collection transformations from proofs

Nested relations, built up from atomic types via product and set types, form a rich data model. Over the last decades the nested relational calculus, NRC, has emerged as a standard language for defining transformations on nested collections. NRC is a strongly-typed functional language which allows building up transformations using tupling and projections, a singleton-former, and a map operation that lifts transformations on tuples to transformations on sets.In this work we describe an alternative declarative method of describing transformations in logic. A formula with distinguished inputs and outputs gives an implicit definition if one can prove that for each input there is only one output that satisfies it. Our main result shows that one can synthesize transformations from proofs that a formula provides an implicit definition, where the proof is in an intuitionistic calculus that captures a natural style of reasoning about nested collections. Our polynomial time synthesis procedure is based on an analog of Craig’s interpolation lemma, starting with a provable containment between terms representing nested collections and generating an NRC expression that interpolates between them.We further show that NRC expressions that implement an implicit definition can be found when there is a classical proof of functionality, not just when there is an intuitionistic one. That is, whenever a formula implicitly defines a transformation, there is an NRC expression that implements it

Bisimilarity and refinement for hybrid(ised) logics

The complexity of modern software systems entails the need for reconfiguration mechanisms governing the dynamic evolution of their execution configurations in response to both external stimulus or internal performance measures. Formally, such systems may be represented by transition systems whose nodes correspond to the different configurations they may assume. Therefore, each node is endowed with, for example, an algebra, or a first-order structure, to precisely characterise the semantics of the services provided in the corresponding configuration. Hybrid logics, which add to the modal description of transition structures the ability to refer to specific states, offer a generic framework to approach the specification and design of this sort of systems. Therefore, the quest for suitable notions of equivalence and refinement between models of hybrid logic specifications becomes fundamental to any design discipline adopting this perspective. This paper contributes to this effort from a distinctive point of view: instead of focussing on a specific hybrid logic, the paper introduces notions of bisimilarity and refinement for hybridised logics, i.e. standard specification logics (e.g. propositional, equational, fuzzy, etc) to which modal and hybrid features were added in a systematic way.FC