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484
Derivability in the Logic of Proofs is Π p 2complete
, 2005
"... The Logic of Proofs realizes the modalities from traditional modal logics with proof polynomials, so an expression ✷F becomes t: F where t is a proof polynomial representing a proof of or evidence for F. The pioneering work on explicating the modal logic S4 is due to S. Artemov and was extended to s ..."
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to several subsystems by V. Brezhnev. In 2000, R. Kuznets presented a Π p 2 algorithm for deducibility in these logics; in the present paper we will show that the deducibility problem is Π p 2complete. (The analogous problem for traditional modal logics is PSPACEcomplete.) Both Kuznets ’ work
A Mixed Linear and NonLinear Logic: Proofs, Terms and Models (Preliminary Report)
, 1994
"... Intuitionistic linear logic regains the expressive power of intuitionistic logic through the ! (`of course') modality. Benton, Bierman, Hyland and de Paiva have given a term assignment system for ILL and an associated notion of categorical model in which the ! modality is modelled by a comonad ..."
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Cited by 114 (5 self)
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satisfying certain extra conditions. Ordinary intuitionistic logic is then modelled in a cartesian closed category which arises as a full subcategory of the category of coalgebras for the comonad. This paper attempts to explain the connection between ILL and IL more directly and symmetrically by giving a
Behavioral theories and the neurophysiology of reward,
 Annu. Rev. Psychol.
, 2006
"... ■ Abstract The functions of rewards are based primarily on their effects on behavior and are less directly governed by the physics and chemistry of input events as in sensory systems. Therefore, the investigation of neural mechanisms underlying reward functions requires behavioral theories that can ..."
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Cited by 187 (0 self)
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, without attempting to provide a complete account of all the studies done. We focus on the activity of single neurons studied by neurophysiological techniques in behaving animals, in particular monkeys, and emphasize the formative role of behavioral theories, such as animal learning theory
Proof Search Issues In Some NonClassical Logics
, 1998
"... This thesis develops techniques and ideas on proof search. Proof search is used with one of two meanings. Proof search can be thought of either as the search for a yes/no answer to a query (theorem proving), or as the search for all proofs of a formula (proof enumeration). This thesis is an investig ..."
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Cited by 45 (2 self)
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calculi such as natural deduction. All the calculi for proof search in this thesis are Gentzen sequent calculi. In Chapter 2, permutation of inference rules for Intuitionistic Linear Logic is studied. A focusing calculus, ILLF, in the style of Andreoli ([And92]) is developed. This calculus allows only one
Logic of Proofs with the strong provability operator
 University of Amsterdam
, 1994
"... Logics with the strong provability operator ": : : is true and provable" together with the proof operators "p is a proof of : : :" are axiomatized. Kripkestyle completeness, decidability and arithmetical completeness of these logics are established. 1 Introduction Logics with th ..."
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Cited by 3 (3 self)
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Logics with the strong provability operator ": : : is true and provable" together with the proof operators "p is a proof of : : :" are axiomatized. Kripkestyle completeness, decidability and arithmetical completeness of these logics are established. 1 Introduction Logics
Reasoning with higherorder abstract syntax in a logical framework
, 2008
"... Logical frameworks based on intuitionistic or linear logics with highertype quantification have been successfully used to give highlevel, modular, and formal specifications of many important judgments in the area of programming languages and inference systems. Given such specifications, it is natu ..."
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Cited by 101 (26 self)
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is an extension of a simple intuitionistic logic that admits higherorder quantification over simply typed λterms (key ingredients for HOAS) as well as induction and a notion of definition. The latter concept of definition is a prooftheoretic device that allows certain theories to be treated as “closed
Mechanizing Programming Logics in Higher Order Logic
 in Current Trends in Hardware Verification and Automated Theorem Proving, ed. P.A. Subrahmanyam and Graham Birtwistle
, 1989
"... Formal reasoning about computer programs can be based directly on the semantics of the programming language, or done in a special purpose logic like Hoare logic. The advantage of the first approach is that it guarantees that the formal reasoning applies to the language being used (it is well known, ..."
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Cited by 65 (3 self)
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, for example, that Hoare’s assignment axiom fails to hold for most programming languages). The advantage of the second approach is that the proofs can be more direct and natural. In this paper, an attempt to get the advantages of both approaches is described. The rules of Hoare logic are mechanically derived
A system of interaction and structure
 ACM TRANSACTIONS ON COMPUTATIONAL LOGIC
, 2004
"... This paper introduces a logical system, called BV, which extends multiplicative linear logic by a noncommutative selfdual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, call ..."
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Cited by 109 (19 self)
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, called the calculus of structures, which is the main contribution of this work. Structures are formulae subject to certain equational laws typical of sequents. The calculus of structures is obtained by generalising the sequent calculus in such a way that a new topdown symmetry of derivations is observed
Linear logic proofs and processes in Petri nets
"... Equivalence between reachability in Petri nets and provability of certain sequent of linear logic has been proven in various ways. This work relates linear logic proofs based on the work of [13] to processes of Petri nets: we prove that from a canonical proof tree, an "equivalent" finite p ..."
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Equivalence between reachability in Petri nets and provability of certain sequent of linear logic has been proven in various ways. This work relates linear logic proofs based on the work of [13] to processes of Petri nets: we prove that from a canonical proof tree, an "equivalent" finite
Transformations as Proofs
, 1993
"... This paper is a companion to [Hen93] which explores in depth the relationship between transformational programming and intuitionistic proofs in a theory of operations and types. Here we concentrate on discussing the extension of the theoretical development to algebraic data types and illustrating th ..."
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the techniques with an example. 2 Introduction and background We are concerned primarily with the task of uncovering the precise mathematical proofs which underlie certain semiformal arguments. In the area of program development the program transformations [BuD77] are an excellent example of semi
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