234 research outputs found
Definite Formulae, Negation-as-Failure, and the Base-extension Semantics of Intuitionistic Propositional Logic
Proof-theoretic semantics (P-tS) is the paradigm of semantics in which
meaning in logic is based on proof (as opposed to truth). A particular instance
of P-tS for intuitionistic propositional logic (IPL) is its base-extension
semantics (B-eS). This semantics is given by a relation called support,
explaining the meaning of the logical constants, which is parameterized by
systems of rules called bases that provide the semantics of atomic
propositions. In this paper, we interpret bases as collections of definite
formulae and use the operational view of the latter as provided by uniform
proof-search -- the proof-theoretic foundation of logic programming (LP) -- to
establish the completeness of IPL for the B-eS. This perspective allows
negation, a subtle issue in P-tS, to be understood in terms of the
negation-as-failure protocol in LP. Specifically, while the denial of a
proposition is traditionally understood as the assertion of its negation, in
B-eS we may understand the denial of a proposition as the failure to find a
proof of it. In this way, assertion and denial are both prime concepts in P-tS.Comment: submitte
Proof-theoretic Semantics and Tactical Proof
The use of logical systems for problem-solving may be as diverse as in
proving theorems in mathematics or in figuring out how to meet up with a
friend. In either case, the problem solving activity is captured by the search
for an \emph{argument}, broadly conceived as a certificate for a solution to
the problem. Crucially, for such a certificate to be a solution, it has be
\emph{valid}, and what makes it valid is that they are well-constructed
according to a notion of inference for the underlying logical system. We
provide a general framework uniformly describing the use of logic as a
mathematics of reasoning in the above sense. We use proof-theoretic validity in
the Dummett-Prawitz tradition to define validity of arguments, and use the
theory of tactical proof to relate arguments, inference, and search.Comment: submitte
From Proof-theoretic Validity to Base-extension Semantics for Intuitionistic Propositional Logic
Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on
\emph{proof} (as opposed to truth). There are two major approaches to P-tS:
proof-theoretic validity (P-tV) and base-extension semantics (B-eS). The former
is a semantics of arguments, and the latter is a semantics of logical constants
in a logic. This paper demonstrates that the B-eS for intuitionistic
propositional logic (IPL) encapsulates the declarative content of a basic
version of P-tV. Such relationships have been considered before yielding
incompleteness results. This paper diverges from these approaches by accounting
for the constructive, hypothetical setup of P-tV. It explicates how the B-eS
for IPL works
Defining Logical Systems via Algebraic Constraints on Proofs
We comprehensively present a program of decomposition of proof systems for
non-classical logics into proof systems for other logics, especially classical
logic, using an algebra of constraints. That is, one recovers a proof system
for a target logic by enriching a proof system for another, typically simpler,
logic with an algebra of constraints that act as correctness conditions on the
latter to capture the former; for example, one may use Boolean algebra to give
constraints in a sequent calculus for classical propositional logic to produce
a sequent calculus for intuitionistic propositional logic. The idea behind such
forms of reduction is to obtain a tool for uniform and modular treatment of
proof theory and provide a bridge between semantics logics and their proof
theory. The article discusses the theoretical background of the project and
provides several illustrations of its work in the field of intuitionistic and
modal logics. The results include the following: a uniform treatment of modular
and cut-free proof systems for a large class of propositional logics; a general
criterion for a novel approach to soundness and completeness of a logic with
respect to a model-theoretic semantics; and a case study deriving a
model-theoretic semantics from a proof-theoretic specification of a logic.Comment: submitte
Simultaneous increasing of thermal conversion efficiency and BMEP while reducing emissions
Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.The Downsizing of internal combustion engines (ICE) is al- ready recognized as a very suitable method for the concurrent enhancement of the indicated fuel conversion efficiency (IFCE) and the break mean effective pressure (BMEP) while also decreasing the CO2 and NOx emissions [1], [2]. The Ultra-Downsizing concept was introduced in [3] as a still higher development stage of ICE and implemented by means of real Atkinson cycles, using asymmetrical crank mechanisms, combined with a very intensive multistage high- pressure turbocharging with intensive intercooling. This allows an increase of ICE performance while keeping the thermal and mechanical strain strength of engine components within the current usual limits. The investigations from [3] were carried out using the simu- lation tool BOOST (AVL Co). The three-stage turbocharging with intensive intercooling used in this process and the release of heat during combustion are controlled by numerous parame- ters. As a consequence, it is very difficult to harmonize them in order to optimize concurrently IFCE, BMEP and emissions. For this reason, the ideal V,p,T-model presented in [4] has been revised, improved and adapted to better meet the BOOST simu- lations. With help of this new, ideal V,p,T-model, it is possible to evaluate adequately the potential for improving the perfor- mance of Ultra-Downsizing.dc201
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a
substructural logic. It focuses on the base-extension semantics (B-eS) for
intuitionistic multiplicative linear logic (IMLL). The starting point is a
review of Sandqvist's B-eS for intuitionistic propositional logic (IPL), for
which we propose an alternative treatment of conjunction that takes the form of
the generalized elimination rule for the connective. The resulting semantics is
shown to be sound and complete. This motivates our main contribution, a B-eS
for IMLL, in which the definitions of the logical constants all take the form
of their elimination rule and for which soundness and completeness are
established.Comment: 27 page
Sized Types for low-level Quantum Metaprogramming
One of the most fundamental aspects of quantum circuit design is the concept
of families of circuits parametrized by an instance size. As in classical
programming, metaprogramming allows the programmer to write entire families of
circuits simultaneously, an ability which is of particular importance in the
context of quantum computing as algorithms frequently use arithmetic over
non-standard word lengths. In this work, we introduce metaQASM, a typed
extension of the openQASM language supporting the metaprogramming of circuit
families. Our language and type system, built around a lightweight
implementation of sized types, supports subtyping over register sizes and is
moreover type-safe. In particular, we prove that our system is strongly
normalizing, and as such any well-typed metaQASM program can be statically
unrolled into a finite circuit.Comment: Presented at Reversible Computation 2019. Final authenticated
publication is available online at
https://doi.org/10.1007/978-3-030-21500-2_
Line orientation adaptation: local or global?
Prolonged exposure to an oriented line shifts the perceived orientation of a subsequently observed line in the opposite direction, a phenomenon known as the tilt aftereffect (TAE). Here we consider whether the TAE for line stimuli is mediated by a mechanism that integrates the local parts of the line into a single global entity prior to the site of adaptation, or the result of the sum of local TAEs acting separately on the parts of the line. To test between these two alternatives we used the fact the TAE transfers almost completely across luminance contrast polarity [1]. We measured the TAE using adaptor and test lines that (1) either alternated in luminance polarity or were of a single polarity, and (2) either alternated in local orientation or were of a single orientation. We reasoned that if the TAE was agnostic to luminance polarity and was parts-based, we should obtain large TAEs using alternating-polarity adaptors with single-polarity tests. However we found that (i) TAEs using one-alternating-polarity adaptors with all-white tests were relatively small, increased slightly for two-alternating-polarity adaptors, and were largest with all-white or all-black adaptors. (ii) however TAEs were relatively large when the test was one-alternating polarity, irrespective of the adaptor type. (iii) The results with orientation closely mirrored those obtained with polarity with the difference that the TAE transfer across orthogonal orientations was weak. Taken together, our results demonstrate that the TAE for lines is mediated by a global shape mechanism that integrates the parts of lines into whole prior to the site of orientation adaptation. The asymmetry in the magnitude of TAE depending on whether the alternating-polarity lines was the adaptor or test can be explained by an imbalance in the population of neurons sensitive to 1st-and 2nd-order lines, with the 2nd-order lines being encoded by a subset of the mechanisms sensitive to 1st-order lines
- …