On Deriving Nested Calculi for Intuitionistic Logics from Semantic Systems

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated labelled calculus

Verifying Temporal Heap Properties Specified via Evolution Logic

This paper addresses the problem of establishing temporal properties of programs written in languages, such as Java, that make extensive use of the heap to allocate--- and deallocate---new objects and threads. Establishing liveness properties is a particularly hard challenge. One of the crucial obstacles is that heap locations have no static names and the number of heap locations is unbounded. The paper presents a framework for the verification of Java-like programs. Unlike classical model checking, which uses propositional temporal logic, we use first-order temporal logic to specify temporal properties of heap evolutions; this logic allows domain changes to be expressed, which permits allocation and deallocation to be modelled naturally. The paper also presents an abstract-interpretation algorithm that automatically verifies temporal properties expressed using the logic

A Tableaux Calculus for Reducing Proof Size

A tableau calculus is proposed, based on a compressed representation of clauses, where literals sharing a similar shape may be merged. The inferences applied on these literals are fused when possible, which reduces the size of the proof. It is shown that the obtained proof procedure is sound, refutationally complete and allows to reduce the size of the tableau by an exponential factor. The approach is compatible with all usual refinements of tableaux.Comment: Technical Repor

Electronic Trap Microscopy - A New Mode for Scanning Electron Microscopy (SEM)

Insulating layers on conducting substrate are investigated by means of secondary electron field emission SEFE in a digital SEM. The kinetics of charge storage and release with time and temperature are controlled and recorded by an external computer.The evaluation is performed pixel-wise with respect to electronic trap concentration nt0, trap capture cross section σc and thermal activation energy Et. Mapping of these trap parameters indicates hidden inhomogenities, defects and pre-treatments of the dielectric layers as well as the pattern of thermal bleaching and release of electrons. The latter ones appear as inhomogeneous processes starting with blinking centers and increasing their concentration with time and temperature

Proving Craig and Lyndon Interpolation Using Labelled Sequent Calculi

We have recently presented a general method of proving the fundamental logical properties of Craig and Lyndon Interpolation (IPs) by induction on derivations in a wide class of internal sequent calculi, including sequents, hypersequents, and nested sequents. Here we adapt the method to a more general external formalism of labelled sequents and provide sufficient criteria on the Kripke-frame characterization of a logic that guarantee the IPs. In particular, we show that classes of frames definable by quantifier-free Horn formulas correspond to logics with the IPs. These criteria capture the modal cube and the infinite family of transitive Geach logics

Explicit Evidence Systems with Common Knowledge

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal explicit evidence logic, which is a two-agent version of LP. We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic

Prenex Separation Logic with One Selector Field

International audienceWe show that infinite satisfiability can be reduced to finite satisfiabil-ity for all prenex formulas of Separation Logic with k ≥ 1 selector fields (SL k). This fact entails the decidability of the finite and infinite satisfiability problems for the class of prenex formulas of SL 1 , by reduction to the first-order theory of a single unary function symbol and an arbitrary number of unary predicate symbols. We also prove that the complexity of this fragment is not elementary recursive, by reduction from the first-order theory of one unary function symbol. Finally, we prove that the Bernays-Schönfinkel-Ramsey fragment of prenex SL 1 formulas with quantifier prefix in the language ∃ * ∀ * is PSPACE-complete

Towards a Proof Theory of G\"odel Modal Logics

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish completeness and complexity results for these fragments

HIV-1 Tat causes cognitive deficits and selective loss of parvalbumin, somatostatin, and neuronal nitric oxide synthase expressing hippocampal CA1 interneuron subpopulations

Memory deficits are characteristic of HIV-associated neurocognitive disorders (HAND) and co-occur with hippocampal pathology. The HIV-1 transactivator of transcription (Tat), a regulatory protein, plays a significant role in these events, but the cellular mechanisms involved are poorly understood. Within the hippocampus, diverse populations of interneurons form complex networks; even subtle disruptions can drastically alter synaptic output, resulting in behavioral dysfunction. We hypothesized that HIV-1 Tat would impair cognitive behavior and injure specific hippocampal interneuron subtypes. Male transgenic mice that inducibly expressed HIV-1 Tat (or non-expressing controls) were assessed for cognitive behavior or had hippocampal CA1 subregions evaluated via interneuron subpopulation markers. Tat exposure decreased spatial memory in a Barnes maze and mnemonic performance in a novel object recognition test. Tat reduced the percentage of neurons expressing neuronal nitric oxide synthase (nNOS) without neuropeptide Y immunoreactivity in the stratum pyramidale and the stratum radiatum, parvalbumin in the stratum pyramidale, and somatostatin in the stratum oriens, which are consistent with reductions in interneuron-specific interneuron type 3 (IS3), bistratified, and oriens-lacunosum-moleculare interneurons, respectively. The findings reveal that an interconnected ensemble of CA1 nNOS-expressing interneurons, the IS3 cells, as well as subpopulations of parvalbumin- and somatostatin-expressing interneurons are preferentially vulnerable to HIV-1 Tat. Importantly, the susceptible interneurons form a microcircuit thought to be involved in feedback inhibition of CA1 pyramidal cells and gating of CA1 pyramidal cell inputs. The identification of vulnerable CA1 hippocampal interneurons may provide novel insight into the basic mechanisms underlying key functional and neurobehavioral deficits associated with HAND