# Cut Elimination for Weak Modal Grzegorczyk Logic via Non-Well

Apr 3, 2018 - We present a sequent calculus for the weak Grzegorczyk logic Go allowing ... sequent calculus allowing non-well-founded proofs Goâ and...

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Apr 3, 2018 - the closed ball with center x and radius r. Recall that .... Let us call a pair of â-proofs (Ï,Ï) a cut pair if Ï is an â-proof of the ..... u(Ï0,liCâD(Ï)).

Mar 17, 2011 - explicitly been left as open problems [13]; moreover, our coNP upper bounds for CKCEM and CKIDCEM ... sequent Î.) Moreover, the format of the rules in op.cit. does not allow for the introduction of more than ..... we need to consider,

Mar 17, 2011 - treatment of our calculus using a dynamic programming approach in the spirit of ... only so-called canonical rules, i.e., left and right introduction.

Sep 1, 2015 - This gives us a way to make a small improvement in our substitution, by adding the information that we can interpret câx Ï(t) as (the value of) u; the sequence of substitutions resulting from this process of successive improvements i

IT University of Copenhagen [email protected] We study cut elimination for a multifocused variant of full linear logic in the sequent calculus. The multifocused normal ...

Jun 14, 2016 - The resulting preproof is denoted P0. Any main formula of rules (BI) and. (w) in P0 is in Î 1. 2 â© Î£1. 2, and Î· = I for any main formula âXÎ·F of rules (c) in. P0. A stack function sck0 together with types of vacuous (âI-red) i

Sep 30, 2010 - Phone: +61 (0)2 6125 5992. ... in the deductive system under study. ..... Since z and s y are not unifiable, the eqL rule above has empty premise ...

Jun 29, 2010 - Bi-Intuitionistic Tense Logic. Rajeev GorÃ©, Linda Postniece and Alwen Tiu. Logic and Computation Group, School of Computer Science.

Jan 20, 2008 - LG serves as the core logic for a more expressive logic, LGÏ, which is obtained by adding rules for fixed points, equality and induction to LG.

Jan 20, 2008 - axiom B â¡ âx.B, where x is not free in B. We show that by adopting the ..... Let us consider, for example, a definition clause for lists. We first introduce a type .... Suppose Î  ends with âL: this case is dual to the previous o

Nov 13, 2017 - Providing a cut-free sequent calculus for S5 has a long history. The efforts in this direction are numerous, and each of them presents some difficulties. In this paper, we present a sequent calculus system for modal logic S5. It has in

Jan 27, 2018 - Let Ïk(I + 1) denote the tower of Ï with the next epsilon number ÎµI+1 = sup{Ïk(I + 1) ... whose order type is the next epsilon number ÎµÏ0+1 to the order type Ï0 of the class of ordinals in a transitive ...... Definition 3.5 Give

The two most important results in the proof theory of linear logic [6] are the admissibility of the cut rule, and the ...... These de doctorat, UniversitÃ© Aix-Marseille II.

Dec 25, 2013 - The proposal was a generalization of a so-called arbitrary public announce- ment logic with an operator for âÏ holds ...... of Logic, Language, and Information, 6:147â169, 1997. [25] J. Hales. Refinement quantifiers for logics of

Apr 1, 2014 - Definition 2.1 The syntax of modal logic ML is inductively defined by the following grammar in extended Backus Naur form: Ï ::= p | p | Ï â§ Ï | Ï â¨ Ï | â¸Ï | â·Ï. The syntax of modal dependence logic MDL is defined by .....

May 16, 2014 - We prove that this general higher dimensional modal logic (HDML) is decidable and we define an axiomatic system for it. .... The cubical laws account for the geometry (concurrency) of the HDAs; there are four kinds of cubical laws depe

Jul 8, 2008 - Instituto Argentino de MatemÃ¡tica (IAM). Saavedra 15 - 3er Piso - 1083 Buenos Aires, Argentina. 3. ..... taking into account the following considerations: 1) Propositions about the properties of the ... From the precedent item and taki

Oct 10, 2014 - 2 Dipartimento di Matematica e Informatica â Universita di Ferrara. Via Saragat 1, 44122, .... on managing large networks, it has become clear that often the same factor appears repeatedly in the ..... Moreover, we did a scalability

Oct 24, 2002 - This means that you get a system that proves the same logic, but all its rules can only be applied in a finite ... Prove a stronger form of consistency, like: you can't have a proof of R and another of R at the same .... Springer-Verla

Jan 16, 2014 - logic is PSPACE-complete and that the complexity drops to the third level of the polynomial hierarchy if we then disallow disjunction. In this way we completely classifiy the computational complexity of the satisfiabil- ity problem for

Finally, we speculate on their computational interpretation. I. INTRODUCTION. The study of modal Î»-calculi, and the modal logics asso- ciated with them through the Curry-Howard correspondence. [1]â[3] began at the dawn of the 1990s, heralded by th

Mar 23, 2010 - different ways to define graphs and graph transformation. We consider ...... G. Aucher, P. Balbiani, L. FariËnas Del Cerro, and A. Herzig. Global ...

Feb 28, 2014 - March 4, 2014. Abstract. We define the notion of a model of higher-order modal logic in an arbitrary elementary topos E. In contrast to the well-known in- terpretation of .... In this way, the topos semantics formulated in terms of a g

Kleene's T-predicate, which says that program e on input n halts and outputs a code for the halting computation .... II, III, VI, IX, X, the formulas can be any modal formulas in the signature of the membership relation, which ...... say that a formu