13 research outputs found

    Proof complexity of intuitionistic implicational formulas

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    Abstract We study implicational formulas in the context of proof complexity of intuitionistic propositional logic (IPC). On the one hand, we give an efficient transformation of tautologies to implicational tautologies that preserves the lengths of intuitionistic extended Frege (EF ) or substitution Frege (SF ) proofs up to a polynomial. On the other hand, EF proofs in the implicational fragment of IPC polynomially simulate full intuitionistic logic for implicational tautologies. The results also apply to other fragments of other superintuitionistic logics under certain conditions. In particular, the exponential lower bounds on the length of intuitionistic EF proofs by Hrubeš [9], generalized to exponential separation between EF and SF systems in superintuitionistic logics of unbounded branching by Jeřábe

    Order algebraizable logics

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    AbstractThis paper develops an order-theoretic generalization of Blok and Pigozziʼs notion of an algebraizable logic. Unavoidably, the ordered model class of a logic, when it exists, is not unique. For uniqueness, the definition must be relativized, either syntactically or semantically. In sentential systems, for instance, the order algebraization process may be required to respect a given but arbitrary polarity on the signature. With every deductive filter of an algebra of the pertinent type, the polarity associates a reflexive and transitive relation called a Leibniz order, analogous to the Leibniz congruence of abstract algebraic logic (AAL). Some core results of AAL are extended here to sentential systems with a polarity. In particular, such a system is order algebraizable if the Leibniz order operator has the following four independent properties: (i) it is injective, (ii) it is isotonic, (iii) it commutes with the inverse image operator of any algebraic homomorphism, and (iv) it produces anti-symmetric orders when applied to filters that define reduced matrix models. Conversely, if a sentential system is order algebraizable in some way, then the order algebraization process naturally induces a polarity for which the Leibniz order operator has properties (i)–(iv)

    An algebraic study of residuated ordered monoids and logics without exchange and contraction.

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    Thesis (Ph.D.)-University of Natal, Durban, 1998.Please refer to the thesis for the abstract

    Use of proof planning in normalisation

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    Automated Reasoning

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    This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

    On the metatheory of linguistics

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    Wurm C. On the metatheory of linguistics. Bielefeld: UB Bielefeld; 2013

    Varieties of residuated lattices

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