On the Herbrand content of LK

We present a structural representation of the Herbrand content of LK-proofs with cuts of complexity prenex Sigma-2/Pi-2. The representation takes the form of a typed non-deterministic tree grammar of order 2 which generates a finite language of first-order terms that appear in the Herbrand expansions obtained through cut-elimination. In particular, for every Gentzen-style reduction between LK-proofs we study the induced grammars and classify the cases in which language equality and inclusion hold.Comment: In Proceedings CL&C 2016, arXiv:1606.0582

On closure ordinals for the modal mu-calculus

The closure ordinal of a formula of modal mu-calculus mu X phi is the least ordinal kappa, if it exists, such that the denotation of the formula and the kappa-th iteration of the monotone operator induced by phi coincide across all transition systems (finite and infinite). It is known that for every alpha < omega^2 there is a formula phi of modal logic such that mu X phi has closure ordinal alpha (Czarnecki 2010). We prove that the closure ordinals arising from the alternation-free fragment of modal mu-calculus (the syntactic class capturing Sigma_2 cap Pi_2) are bounded by omega^2. In this logic satisfaction can be characterised in terms of the existence of tableaux, trees generated by systematically breaking down formulae into their constituents according to the semantics of the calculus. To obtain optimal upper bounds we utilise the connection between closure ordinals of formulae and embedded order-types of the corresponding tableaux

On closure ordinals for the modal mu-calculus

The closure ordinal of a formula of modal mu-calculus mu X phi is the least ordinal kappa, if it exists, such that the denotation of the formula and the kappa-th iteration of the monotone operator induced by phi coincide across all transition systems (finite and infinite). It is known that for every alpha < omega^2 there is a formula phi of modal logic such that mu X phi has closure ordinal alpha (Czarnecki 2010). We prove that the closure ordinals arising from the alternation-free fragment of modal mu-calculus (the syntactic class capturing Sigma_2 cap Pi_2) are bounded by omega^2. In this logic satisfaction can be characterised in terms of the existence of tableaux, trees generated by systematically breaking down formulae into their constituents according to the semantics of the calculus. To obtain optimal upper bounds we utilise the connection between closure ordinals of formulae and embedded order-types of the corresponding tableaux

Finitary proof systems for Kozen’s μ.

We present three finitary cut-free sequent calculi for the modal [my]-calculus. Two of these derive annotated sequents in the style of Stirling’s ‘tableau proof system with names’ (4236) and feature special inferences that discharge open assumptions. The third system is a variant of Kozen’s axiomatisation in which cut is replaced by a strengthening of the v-induction inference rule. Soundness and completeness for the three systems is proved by establishing a sequence of embeddings between the calculi, starting at Stirling’s tableau-proofs and ending at the original axiomatisation of the [my]-calculus due to Kozen. As a corollary we obtain a completeness proof for Kozen’s axiomatisation which avoids the usual detour through automata or games

A Cyclic Proof System for Full Computation Tree Logic

Full Computation Tree Logic, commonly denoted CTL*, is the extension of Linear Temporal Logic LTL by path quantification for reasoning about branching time. In contrast to traditional Computation Tree Logic CTL, the path quantifiers are not bound to specific linear modalities, resulting in a more expressive language. We present a sound and complete hypersequent calculus for CTL*. The proof system is cyclic in the sense that proofs are finite derivation trees with back-edges. A syntactic success condition on non-axiomatic leaves guarantees soundness. Completeness is established by relating cyclic proofs to a natural ill-founded sequent calculus for the logic

Recent Advancements in Aptamer-bioconjugates: Sharpening Stones for Breast and Prostate Cancers Targeting

Breast and prostate cancers are common types of cancers with various strategies, such as chemotherapy and radiotherapy, for their therapy. Since these methods have undesired side effects and poor target affinity, neoteric strategies—known as aptamer-based smart drug delivery systems (SDDSs)—have been developed in recent years to overcome the obstacles of current treatment, and investigated for a clinical trial. The high affinity and versatility of aptamers for binding to the corresponding targets make them highly noticeable agents in the drug delivery domains. In addition to their exceptional benefits, aptamers are able to overcome tumor resistance because of their high selectivity and low toxicity. Furthermore, aptamers can conjugate with various drugs, nanoparticles and antibodies and effectively deliver them to the specific breast and prostate cells. This review highlights the current researches in aptamer-conjugate developments for targeting breast and prostate cancers, with the special focus on the nanoparticle-aptamer bioconjugates, systematic evolution of ligands by exponential enrichment (SELEX) system and SDDS, especially cutting-edge articles from 2008 to present. Finally, the future prospects and challenges are described

Relative computability and the proof-theoretic strength of some theories

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Relative computability and the proof−theoretic strength of some theories

EThOS - Electronic Theses Online ServiceGBUnited Kingdo