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Things that can and things that can't be done in PRA
, 1998
"... It is wellknown by now that large parts of (nonconstructive) mathematical reasoning can be carried out in systems T which are conservative over primitive recursive arithmetic PRA (and even much weaker systems). On the other hand there are principles S of elementary analysis (like the BolzanoW ..."
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It is wellknown by now that large parts of (nonconstructive) mathematical reasoning can be carried out in systems T which are conservative over primitive recursive arithmetic PRA (and even much weaker systems). On the other hand there are principles S of elementary analysis (like the BolzanoWeierstra principle, the existence of a limit superior for bounded sequences etc.) which are known to be equivalent to arithmetical comprehension (relative to T ) and therefore go far beyond the strength of PRA (when added to T ). In this paper
Is mathematics consistent?
, 2003
"... Abstract: A question is proposed whether or not set theory is consistent. We consider a formal set theory S, where we can develop a number theory. As no generality is lost, in the following we consider a number theory that can be regarded as a subsystem of S, and will call it S (0). Definition 1. 1) ..."
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Abstract: A question is proposed whether or not set theory is consistent. We consider a formal set theory S, where we can develop a number theory. As no generality is lost, in the following we consider a number theory that can be regarded as a subsystem of S, and will call it S (0). Definition 1. 1) We assume that a Gödel numbering of the system S (0) is given, and denote a formula with the Gödel number n by An. 2) A (0) (a, b) is a predicate meaning that “a is the Gödel number of a formula A with just one free variable (which we denote by A(a)), and b is the Gödel number of a proof of the formula A(a) in S (0), ” and B (0) (a, c) is a predicate meaning that “a is the Gödel number of a formula A(a), and c is the Gödel number of a proof of the formula ¬A(a) in S (0). ” Here a denotes the formal natural number corresponding to an intuitive natural number a of the meta level. Definition 2. Let P(x1, · · ·.xn) be an intuitivetheoretic predicate. We say that P(x1, · · ·,xn) is numeralwise expressible in the formal system S (0), if there is a formula P(x1, · · ·,xn) with no free variables other than the distinct variables x1, · · ·,xn such that, for each particular ntuple of natural numbers x1, · · ·,xn, the following holds: i) if P(x1, · · ·,xn) is true, then ⊢ P(x1, · · ·,xn). and ii) if P(x1, · · ·,xn) is false, then ⊢ ¬P(x1, · · ·,xn).
λCalculus: Then & Now
, 2012
"... Notes derived from the slides presented at the conferences. A brief amount of text has been added for continuity. The author would be happy to hear reactions and suggestions. ..."
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Notes derived from the slides presented at the conferences. A brief amount of text has been added for continuity. The author would be happy to hear reactions and suggestions.
An intensional concurrent faithful encoding of Turing machines
 Proceedings 7th Interaction and Concurrency Experience
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Syntax Zooming
 Proc. of 3rd Serbian—Hungarian Joint Symposium On Intelligent Systems, Subotica (SISY
, 2005
"... Abstract: We shall present various procedures for the syntax analysis in certain formal systems defined by the user, which are integrated in the proof checker. The flexibility and the applicability of the method lies in the fact that the program treats formal theories as parameters (both axioms and ..."
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Abstract: We shall present various procedures for the syntax analysis in certain formal systems defined by the user, which are integrated in the proof checker. The flexibility and the applicability of the method lies in the fact that the program treats formal theories as parameters (both axioms and derivation rules are parts of the input), so developed algorithms work for any formalism which can be expressed within the language of the predicate logic. 1
(TEL) ÷81436745511, (FAX) +81436742592. Yotaro Nakayama
"... We discuss some consequence relations in DRT useful to discourse semantics. We incorporate some consequence relations into DRT using sequent calculi. We also show some connections of these consequence relations and existing partial logics. Our attempt enables us to display several versions of DRT by ..."
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We discuss some consequence relations in DRT useful to discourse semantics. We incorporate some consequence relations into DRT using sequent calculi. We also show some connections of these consequence relations and existing partial logics. Our attempt enables us to display several versions of DRT by employing different consequence relations. 1.
Decision Procedure for a Fragment of Temporal Logic of Belief and Actions with Quantified Agent and Action Variables
, 2004
"... A decision procedure for a fragment of temporal logic of belief and action with quantified agent and actions variables (T LBAQ) is presented. A language of TLBAQ contains variables and constants for agents and actions. The language of TLBAQ is a subset of language LORA introduced by M. Wooldridge. ..."
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A decision procedure for a fragment of temporal logic of belief and action with quantified agent and actions variables (T LBAQ) is presented. A language of TLBAQ contains variables and constants for agents and actions. The language of TLBAQ is a subset of language LORA introduced by M. Wooldridge. The TLBAQ consists of two components: informational and dynamic. An informational (agent) component of TLBAQ consists of the multimodal logic KD45n extended with restricted occurrences of quantifiers for agent variables. A dynamic component of TLBAQ consists of temporal and action parts. A temporal part of TLBAQ is represented by Computational Tree Logic. An action part is represented by a propositional dynamic logic extended with restricted occurrences of quantifiers for action variables. The language of TLBAQ is convenient to describe properties of rational agents when the number of agents and actions is infinite or is not known in advance. In informational (agent) component of presented decision procedure loop exclusion method instead of loop checking method is proposed. The loop exclusion method corresponds to construction of contractionfree calculus. The presented decision procedure is based on sequent calculus with invertible rules. The calculus contains, along with logical axioms, looptype axioms which are captured in a rather simple way.